ds606_Inferenceforcategoricaldata_lab6_jagdishchhabria’
In August of 2012, news outlets ranging from the Washington Post to the Huffington Post ran a story about the rise of atheism in America. The source for the story was a poll that asked people, “Irrespective of whether you attend a place of worship or not, would you say you are a religious person, not a religious person or a convinced atheist?” This type of question, which asks people to classify themselves in one way or another, is common in polling and generates categorical data. In this lab we take a look at the atheism survey and explore what’s at play when making inference about population proportions using categorical data.
The survey
To access the press release for the poll, conducted by WIN-Gallup International, click on the following link:
Take a moment to review the report then address the following questions.
In the first paragraph, several key findings are reported. Do these percentages appear to be sample statistics (derived from the data sample) or population parameters?
These appear to be sample statistics.
The title of the report is “Global Index of Religiosity and Atheism”. To generalize the report’s findings to the global human population, what must we assume about the sampling method? Does that seem like a reasonable assumption?
We must assume that the sample was randomly drawn. At 50,000 respondents, the size is large enough but still less than 10% of the global population.
The data
Turn your attention to Table 6 (pages 15 and 16), which reports the sample size and response percentages for all 57 countries. While this is a useful format to summarize the data, we will base our analysis on the original data set of individual responses to the survey. Load this data set into R with the following command.
load("more/atheism.RData")- What does each row of Table 6 correspond to? What does each row of
atheismcorrespond to? Each row corresponds to the survey respondents for a given country. Each row of atheism gives the proportion of respondents from the total surveyed in that country, that identified themselves as convinced atheists.
To investigate the link between these two ways of organizing this data, take a look at the estimated proportion of atheists in the United States. Towards the bottom of Table 6, we see that this is 5%. We should be able to come to the same number using the atheism data.
- Using the command below, create a new dataframe called
us12that contains only the rows inatheismassociated with respondents to the 2012 survey from the United States. Next, calculate the proportion of atheist responses. Does it agree with the percentage in Table 6? If not, why?
us12 <- subset(atheism, nationality == "United States" & year == "2012")
#us12Inference on proportions
As was hinted at in Exercise 1, Table 6 provides statistics, that is, calculations made from the sample of 51,927 people. What we’d like, though, is insight into the population parameters. You answer the question, “What proportion of people in your sample reported being atheists?” with a statistic; while the question “What proportion of people on earth would report being atheists” is answered with an estimate of the parameter.
The inferential tools for estimating population proportion are analogous to those used for means in the last chapter: the confidence interval and the hypothesis test.
- Write out the conditions for inference to construct a 95% confidence interval for the proportion of atheists in the United States in 2012. Are you confident all conditions are met?
The conditions of inference are that the sample should be randomly drawn, and that there should be at least 10 yes (i.e. atheists) and 10 no (i.e. non-atheists) answers.
If the conditions for inference are reasonable, we can either calculate the standard error and construct the interval by hand, or allow the inference function to do it for us.
inference(us12$response, est = "proportion", type = "ci", method = "theoretical",
success = "atheist")## Warning: package 'BHH2' was built under R version 3.5.3## Single proportion -- success: atheist
## Summary statistics:
## p_hat = 0.0499 ; n = 1002
## Check conditions: number of successes = 50 ; number of failures = 952
## Standard error = 0.0069
## 95 % Confidence interval = ( 0.0364 , 0.0634 )Note that since the goal is to construct an interval estimate for a proportion, it’s necessary to specify what constitutes a “success”, which here is a response of "atheist".
Although formal confidence intervals and hypothesis tests don’t show up in the report, suggestions of inference appear at the bottom of page 7: “In general, the error margin for surveys of this kind is \(\pm\) 3-5% at 95% confidence”.
Based on the R output, what is the margin of error for the estimate of the proportion of the proportion of atheists in US in 2012?
Margin of error = 0.0634 - 0.0499 = 0.0135 Margin of error = 1.96 * sqrt((0.0499 X 0.9501)/1002)
Using the
inferencefunction, calculate confidence intervals for the proportion of atheists in 2012 in two other countries of your choice, and report the associated margins of error. Be sure to note whether the conditions for inference are met. It may be helpful to create new data sets for each of the two countries first, and then use these data sets in theinferencefunction to construct the confidence intervals.
in12 <- subset(atheism, nationality == "India" & year == "2012")
in12## nationality response year
## 21654 India non-atheist 2012
## 21655 India non-atheist 2012
## 21656 India non-atheist 2012
## 21657 India non-atheist 2012
## 21658 India non-atheist 2012
## 21659 India non-atheist 2012
## 21660 India non-atheist 2012
## 21661 India non-atheist 2012
## 21662 India non-atheist 2012
## 21663 India atheist 2012
## 21664 India non-atheist 2012
## 21665 India non-atheist 2012
## 21666 India non-atheist 2012
## 21667 India non-atheist 2012
## 21668 India non-atheist 2012
## 21669 India non-atheist 2012
## 21670 India non-atheist 2012
## 21671 India non-atheist 2012
## 21672 India non-atheist 2012
## 21673 India non-atheist 2012
## 21674 India non-atheist 2012
## 21675 India non-atheist 2012
## 21676 India non-atheist 2012
## 21677 India non-atheist 2012
## 21678 India non-atheist 2012
## 21679 India non-atheist 2012
## 21680 India non-atheist 2012
## 21681 India non-atheist 2012
## 21682 India non-atheist 2012
## 21683 India non-atheist 2012
## 21684 India non-atheist 2012
## 21685 India non-atheist 2012
## 21686 India non-atheist 2012
## 21687 India non-atheist 2012
## 21688 India non-atheist 2012
## 21689 India non-atheist 2012
## 21690 India non-atheist 2012
## 21691 India non-atheist 2012
## 21692 India non-atheist 2012
## 21693 India non-atheist 2012
## 21694 India non-atheist 2012
## 21695 India non-atheist 2012
## 21696 India non-atheist 2012
## 21697 India non-atheist 2012
## 21698 India non-atheist 2012
## 21699 India non-atheist 2012
## 21700 India non-atheist 2012
## 21701 India non-atheist 2012
## 21702 India non-atheist 2012
## 21703 India non-atheist 2012
## 21704 India non-atheist 2012
## 21705 India non-atheist 2012
## 21706 India non-atheist 2012
## 21707 India non-atheist 2012
## 21708 India non-atheist 2012
## 21709 India non-atheist 2012
## 21710 India non-atheist 2012
## 21711 India non-atheist 2012
## 21712 India non-atheist 2012
## 21713 India non-atheist 2012
## 21714 India non-atheist 2012
## 21715 India atheist 2012
## 21716 India non-atheist 2012
## 21717 India non-atheist 2012
## 21718 India non-atheist 2012
## 21719 India non-atheist 2012
## 21720 India non-atheist 2012
## 21721 India atheist 2012
## 21722 India atheist 2012
## 21723 India non-atheist 2012
## 21724 India non-atheist 2012
## 21725 India non-atheist 2012
## 21726 India non-atheist 2012
## 21727 India non-atheist 2012
## 21728 India non-atheist 2012
## 21729 India non-atheist 2012
## 21730 India non-atheist 2012
## 21731 India non-atheist 2012
## 21732 India non-atheist 2012
## 21733 India non-atheist 2012
## 21734 India non-atheist 2012
## 21735 India non-atheist 2012
## 21736 India non-atheist 2012
## 21737 India non-atheist 2012
## 21738 India non-atheist 2012
## 21739 India non-atheist 2012
## 21740 India non-atheist 2012
## 21741 India non-atheist 2012
## 21742 India non-atheist 2012
## 21743 India non-atheist 2012
## 21744 India non-atheist 2012
## 21745 India non-atheist 2012
## 21746 India non-atheist 2012
## 21747 India non-atheist 2012
## 21748 India non-atheist 2012
## 21749 India non-atheist 2012
## 21750 India non-atheist 2012
## 21751 India non-atheist 2012
## 21752 India non-atheist 2012
## 21753 India non-atheist 2012
## 21754 India atheist 2012
## 21755 India non-atheist 2012
## 21756 India non-atheist 2012
## 21757 India non-atheist 2012
## 21758 India non-atheist 2012
## 21759 India non-atheist 2012
## 21760 India non-atheist 2012
## 21761 India non-atheist 2012
## 21762 India non-atheist 2012
## 21763 India non-atheist 2012
## 21764 India non-atheist 2012
## 21765 India non-atheist 2012
## 21766 India non-atheist 2012
## 21767 India non-atheist 2012
## 21768 India non-atheist 2012
## 21769 India non-atheist 2012
## 21770 India non-atheist 2012
## 21771 India non-atheist 2012
## 21772 India non-atheist 2012
## 21773 India non-atheist 2012
## 21774 India non-atheist 2012
## 21775 India non-atheist 2012
## 21776 India non-atheist 2012
## 21777 India non-atheist 2012
## 21778 India non-atheist 2012
## 21779 India non-atheist 2012
## 21780 India non-atheist 2012
## 21781 India atheist 2012
## 21782 India non-atheist 2012
## 21783 India non-atheist 2012
## 21784 India non-atheist 2012
## 21785 India non-atheist 2012
## 21786 India non-atheist 2012
## 21787 India non-atheist 2012
## 21788 India non-atheist 2012
## 21789 India non-atheist 2012
## 21790 India non-atheist 2012
## 21791 India non-atheist 2012
## 21792 India non-atheist 2012
## 21793 India non-atheist 2012
## 21794 India non-atheist 2012
## 21795 India non-atheist 2012
## 21796 India non-atheist 2012
## 21797 India non-atheist 2012
## 21798 India atheist 2012
## 21799 India non-atheist 2012
## 21800 India non-atheist 2012
## 21801 India non-atheist 2012
## 21802 India non-atheist 2012
## 21803 India non-atheist 2012
## 21804 India non-atheist 2012
## 21805 India non-atheist 2012
## 21806 India non-atheist 2012
## 21807 India non-atheist 2012
## 21808 India non-atheist 2012
## 21809 India non-atheist 2012
## 21810 India non-atheist 2012
## 21811 India non-atheist 2012
## 21812 India non-atheist 2012
## 21813 India non-atheist 2012
## 21814 India non-atheist 2012
## 21815 India non-atheist 2012
## 21816 India non-atheist 2012
## 21817 India non-atheist 2012
## 21818 India non-atheist 2012
## 21819 India non-atheist 2012
## 21820 India atheist 2012
## 21821 India non-atheist 2012
## 21822 India non-atheist 2012
## 21823 India non-atheist 2012
## 21824 India non-atheist 2012
## 21825 India non-atheist 2012
## 21826 India non-atheist 2012
## 21827 India non-atheist 2012
## 21828 India non-atheist 2012
## 21829 India non-atheist 2012
## 21830 India non-atheist 2012
## 21831 India non-atheist 2012
## 21832 India non-atheist 2012
## 21833 India non-atheist 2012
## 21834 India non-atheist 2012
## 21835 India non-atheist 2012
## 21836 India non-atheist 2012
## 21837 India non-atheist 2012
## 21838 India non-atheist 2012
## 21839 India non-atheist 2012
## 21840 India non-atheist 2012
## 21841 India non-atheist 2012
## 21842 India non-atheist 2012
## 21843 India non-atheist 2012
## 21844 India non-atheist 2012
## 21845 India non-atheist 2012
## 21846 India non-atheist 2012
## 21847 India non-atheist 2012
## 21848 India non-atheist 2012
## 21849 India non-atheist 2012
## 21850 India non-atheist 2012
## 21851 India non-atheist 2012
## 21852 India non-atheist 2012
## 21853 India non-atheist 2012
## 21854 India non-atheist 2012
## 21855 India non-atheist 2012
## 21856 India non-atheist 2012
## 21857 India non-atheist 2012
## 21858 India non-atheist 2012
## 21859 India non-atheist 2012
## 21860 India non-atheist 2012
## 21861 India non-atheist 2012
## 21862 India non-atheist 2012
## 21863 India non-atheist 2012
## 21864 India non-atheist 2012
## 21865 India atheist 2012
## 21866 India non-atheist 2012
## 21867 India non-atheist 2012
## 21868 India non-atheist 2012
## 21869 India non-atheist 2012
## 21870 India non-atheist 2012
## 21871 India non-atheist 2012
## 21872 India non-atheist 2012
## 21873 India non-atheist 2012
## 21874 India non-atheist 2012
## 21875 India non-atheist 2012
## 21876 India non-atheist 2012
## 21877 India non-atheist 2012
## 21878 India non-atheist 2012
## 21879 India non-atheist 2012
## 21880 India non-atheist 2012
## 21881 India non-atheist 2012
## 21882 India non-atheist 2012
## 21883 India non-atheist 2012
## 21884 India non-atheist 2012
## 21885 India non-atheist 2012
## 21886 India non-atheist 2012
## 21887 India non-atheist 2012
## 21888 India non-atheist 2012
## 21889 India non-atheist 2012
## 21890 India non-atheist 2012
## 21891 India non-atheist 2012
## 21892 India non-atheist 2012
## 21893 India non-atheist 2012
## 21894 India non-atheist 2012
## 21895 India non-atheist 2012
## 21896 India atheist 2012
## 21897 India non-atheist 2012
## 21898 India non-atheist 2012
## 21899 India non-atheist 2012
## 21900 India non-atheist 2012
## 21901 India non-atheist 2012
## 21902 India non-atheist 2012
## 21903 India non-atheist 2012
## 21904 India non-atheist 2012
## 21905 India non-atheist 2012
## 21906 India non-atheist 2012
## 21907 India non-atheist 2012
## 21908 India non-atheist 2012
## 21909 India non-atheist 2012
## 21910 India non-atheist 2012
## 21911 India non-atheist 2012
## 21912 India non-atheist 2012
## 21913 India non-atheist 2012
## 21914 India non-atheist 2012
## 21915 India non-atheist 2012
## 21916 India non-atheist 2012
## 21917 India non-atheist 2012
## 21918 India non-atheist 2012
## 21919 India non-atheist 2012
## 21920 India non-atheist 2012
## 21921 India non-atheist 2012
## 21922 India non-atheist 2012
## 21923 India non-atheist 2012
## 21924 India non-atheist 2012
## 21925 India non-atheist 2012
## 21926 India non-atheist 2012
## 21927 India non-atheist 2012
## 21928 India non-atheist 2012
## 21929 India non-atheist 2012
## 21930 India non-atheist 2012
## 21931 India non-atheist 2012
## 21932 India non-atheist 2012
## 21933 India non-atheist 2012
## 21934 India non-atheist 2012
## 21935 India non-atheist 2012
## 21936 India non-atheist 2012
## 21937 India non-atheist 2012
## 21938 India non-atheist 2012
## 21939 India non-atheist 2012
## 21940 India non-atheist 2012
## 21941 India non-atheist 2012
## 21942 India non-atheist 2012
## 21943 India non-atheist 2012
## 21944 India non-atheist 2012
## 21945 India non-atheist 2012
## 21946 India non-atheist 2012
## 21947 India non-atheist 2012
## 21948 India non-atheist 2012
## 21949 India non-atheist 2012
## 21950 India non-atheist 2012
## 21951 India atheist 2012
## 21952 India non-atheist 2012
## 21953 India non-atheist 2012
## 21954 India non-atheist 2012
## 21955 India non-atheist 2012
## 21956 India non-atheist 2012
## 21957 India non-atheist 2012
## 21958 India non-atheist 2012
## 21959 India non-atheist 2012
## 21960 India atheist 2012
## 21961 India non-atheist 2012
## 21962 India non-atheist 2012
## 21963 India non-atheist 2012
## 21964 India non-atheist 2012
## 21965 India non-atheist 2012
## 21966 India non-atheist 2012
## 21967 India non-atheist 2012
## 21968 India non-atheist 2012
## 21969 India non-atheist 2012
## 21970 India non-atheist 2012
## 21971 India atheist 2012
## 21972 India non-atheist 2012
## 21973 India non-atheist 2012
## 21974 India non-atheist 2012
## 21975 India non-atheist 2012
## 21976 India non-atheist 2012
## 21977 India non-atheist 2012
## 21978 India non-atheist 2012
## 21979 India non-atheist 2012
## 21980 India non-atheist 2012
## 21981 India non-atheist 2012
## 21982 India non-atheist 2012
## 21983 India non-atheist 2012
## 21984 India non-atheist 2012
## 21985 India non-atheist 2012
## 21986 India non-atheist 2012
## 21987 India non-atheist 2012
## 21988 India non-atheist 2012
## 21989 India non-atheist 2012
## 21990 India non-atheist 2012
## 21991 India non-atheist 2012
## 21992 India non-atheist 2012
## 21993 India non-atheist 2012
## 21994 India non-atheist 2012
## 21995 India non-atheist 2012
## 21996 India non-atheist 2012
## 21997 India non-atheist 2012
## 21998 India non-atheist 2012
## 21999 India atheist 2012
## 22000 India non-atheist 2012
## 22001 India non-atheist 2012
## 22002 India non-atheist 2012
## 22003 India non-atheist 2012
## 22004 India non-atheist 2012
## 22005 India non-atheist 2012
## 22006 India non-atheist 2012
## 22007 India non-atheist 2012
## 22008 India non-atheist 2012
## 22009 India non-atheist 2012
## 22010 India non-atheist 2012
## 22011 India non-atheist 2012
## 22012 India non-atheist 2012
## 22013 India non-atheist 2012
## 22014 India non-atheist 2012
## 22015 India non-atheist 2012
## 22016 India non-atheist 2012
## 22017 India non-atheist 2012
## 22018 India non-atheist 2012
## 22019 India non-atheist 2012
## 22020 India non-atheist 2012
## 22021 India non-atheist 2012
## 22022 India non-atheist 2012
## 22023 India non-atheist 2012
## 22024 India non-atheist 2012
## 22025 India non-atheist 2012
## 22026 India non-atheist 2012
## 22027 India non-atheist 2012
## 22028 India non-atheist 2012
## 22029 India non-atheist 2012
## 22030 India non-atheist 2012
## 22031 India non-atheist 2012
## 22032 India non-atheist 2012
## 22033 India non-atheist 2012
## 22034 India non-atheist 2012
## 22035 India non-atheist 2012
## 22036 India non-atheist 2012
## 22037 India non-atheist 2012
## 22038 India non-atheist 2012
## 22039 India non-atheist 2012
## 22040 India non-atheist 2012
## 22041 India non-atheist 2012
## 22042 India non-atheist 2012
## 22043 India non-atheist 2012
## 22044 India non-atheist 2012
## 22045 India non-atheist 2012
## 22046 India non-atheist 2012
## 22047 India non-atheist 2012
## 22048 India non-atheist 2012
## 22049 India non-atheist 2012
## 22050 India non-atheist 2012
## 22051 India atheist 2012
## 22052 India atheist 2012
## 22053 India non-atheist 2012
## 22054 India non-atheist 2012
## 22055 India non-atheist 2012
## 22056 India non-atheist 2012
## 22057 India non-atheist 2012
## 22058 India non-atheist 2012
## 22059 India non-atheist 2012
## 22060 India non-atheist 2012
## 22061 India non-atheist 2012
## 22062 India non-atheist 2012
## 22063 India non-atheist 2012
## 22064 India non-atheist 2012
## 22065 India non-atheist 2012
## 22066 India non-atheist 2012
## 22067 India non-atheist 2012
## 22068 India non-atheist 2012
## 22069 India non-atheist 2012
## 22070 India non-atheist 2012
## 22071 India non-atheist 2012
## 22072 India non-atheist 2012
## 22073 India non-atheist 2012
## 22074 India non-atheist 2012
## 22075 India non-atheist 2012
## 22076 India non-atheist 2012
## 22077 India non-atheist 2012
## 22078 India non-atheist 2012
## 22079 India non-atheist 2012
## 22080 India non-atheist 2012
## 22081 India non-atheist 2012
## 22082 India non-atheist 2012
## 22083 India non-atheist 2012
## 22084 India non-atheist 2012
## 22085 India non-atheist 2012
## 22086 India non-atheist 2012
## 22087 India non-atheist 2012
## 22088 India non-atheist 2012
## 22089 India non-atheist 2012
## 22090 India non-atheist 2012
## 22091 India non-atheist 2012
## 22092 India non-atheist 2012
## 22093 India non-atheist 2012
## 22094 India non-atheist 2012
## 22095 India non-atheist 2012
## 22096 India non-atheist 2012
## 22097 India non-atheist 2012
## 22098 India non-atheist 2012
## 22099 India non-atheist 2012
## 22100 India non-atheist 2012
## 22101 India non-atheist 2012
## 22102 India non-atheist 2012
## 22103 India non-atheist 2012
## 22104 India non-atheist 2012
## 22105 India non-atheist 2012
## 22106 India non-atheist 2012
## 22107 India atheist 2012
## 22108 India non-atheist 2012
## 22109 India non-atheist 2012
## 22110 India non-atheist 2012
## 22111 India non-atheist 2012
## 22112 India non-atheist 2012
## 22113 India non-atheist 2012
## 22114 India non-atheist 2012
## 22115 India non-atheist 2012
## 22116 India non-atheist 2012
## 22117 India non-atheist 2012
## 22118 India non-atheist 2012
## 22119 India non-atheist 2012
## 22120 India non-atheist 2012
## 22121 India non-atheist 2012
## 22122 India non-atheist 2012
## 22123 India non-atheist 2012
## 22124 India non-atheist 2012
## 22125 India non-atheist 2012
## 22126 India non-atheist 2012
## 22127 India non-atheist 2012
## 22128 India non-atheist 2012
## 22129 India non-atheist 2012
## 22130 India non-atheist 2012
## 22131 India atheist 2012
## 22132 India non-atheist 2012
## 22133 India non-atheist 2012
## 22134 India non-atheist 2012
## 22135 India non-atheist 2012
## 22136 India non-atheist 2012
## 22137 India non-atheist 2012
## 22138 India non-atheist 2012
## 22139 India non-atheist 2012
## 22140 India non-atheist 2012
## 22141 India non-atheist 2012
## 22142 India non-atheist 2012
## 22143 India non-atheist 2012
## 22144 India non-atheist 2012
## 22145 India non-atheist 2012
## 22146 India non-atheist 2012
## 22147 India non-atheist 2012
## 22148 India non-atheist 2012
## 22149 India non-atheist 2012
## 22150 India non-atheist 2012
## 22151 India non-atheist 2012
## 22152 India non-atheist 2012
## 22153 India non-atheist 2012
## 22154 India non-atheist 2012
## 22155 India non-atheist 2012
## 22156 India non-atheist 2012
## 22157 India non-atheist 2012
## 22158 India non-atheist 2012
## 22159 India non-atheist 2012
## 22160 India non-atheist 2012
## 22161 India non-atheist 2012
## 22162 India non-atheist 2012
## 22163 India non-atheist 2012
## 22164 India non-atheist 2012
## 22165 India non-atheist 2012
## 22166 India non-atheist 2012
## 22167 India non-atheist 2012
## 22168 India non-atheist 2012
## 22169 India non-atheist 2012
## 22170 India non-atheist 2012
## 22171 India non-atheist 2012
## 22172 India non-atheist 2012
## 22173 India non-atheist 2012
## 22174 India non-atheist 2012
## 22175 India non-atheist 2012
## 22176 India non-atheist 2012
## 22177 India non-atheist 2012
## 22178 India non-atheist 2012
## 22179 India non-atheist 2012
## 22180 India non-atheist 2012
## 22181 India non-atheist 2012
## 22182 India non-atheist 2012
## 22183 India non-atheist 2012
## 22184 India non-atheist 2012
## 22185 India non-atheist 2012
## 22186 India non-atheist 2012
## 22187 India non-atheist 2012
## 22188 India non-atheist 2012
## 22189 India non-atheist 2012
## 22190 India non-atheist 2012
## 22191 India non-atheist 2012
## 22192 India non-atheist 2012
## 22193 India non-atheist 2012
## 22194 India non-atheist 2012
## 22195 India non-atheist 2012
## 22196 India non-atheist 2012
## 22197 India non-atheist 2012
## 22198 India non-atheist 2012
## 22199 India non-atheist 2012
## 22200 India non-atheist 2012
## 22201 India non-atheist 2012
## 22202 India non-atheist 2012
## 22203 India non-atheist 2012
## 22204 India non-atheist 2012
## 22205 India non-atheist 2012
## 22206 India non-atheist 2012
## 22207 India non-atheist 2012
## 22208 India non-atheist 2012
## 22209 India non-atheist 2012
## 22210 India non-atheist 2012
## 22211 India non-atheist 2012
## 22212 India non-atheist 2012
## 22213 India non-atheist 2012
## 22214 India non-atheist 2012
## 22215 India non-atheist 2012
## 22216 India non-atheist 2012
## 22217 India non-atheist 2012
## 22218 India atheist 2012
## 22219 India non-atheist 2012
## 22220 India non-atheist 2012
## 22221 India non-atheist 2012
## 22222 India non-atheist 2012
## 22223 India non-atheist 2012
## 22224 India non-atheist 2012
## 22225 India non-atheist 2012
## 22226 India non-atheist 2012
## 22227 India non-atheist 2012
## 22228 India non-atheist 2012
## 22229 India non-atheist 2012
## 22230 India non-atheist 2012
## 22231 India non-atheist 2012
## 22232 India non-atheist 2012
## 22233 India non-atheist 2012
## 22234 India non-atheist 2012
## 22235 India non-atheist 2012
## 22236 India non-atheist 2012
## 22237 India non-atheist 2012
## 22238 India non-atheist 2012
## 22239 India non-atheist 2012
## 22240 India non-atheist 2012
## 22241 India non-atheist 2012
## 22242 India atheist 2012
## 22243 India atheist 2012
## 22244 India non-atheist 2012
## 22245 India non-atheist 2012
## 22246 India non-atheist 2012
## 22247 India non-atheist 2012
## 22248 India non-atheist 2012
## 22249 India non-atheist 2012
## 22250 India non-atheist 2012
## 22251 India non-atheist 2012
## 22252 India non-atheist 2012
## 22253 India non-atheist 2012
## 22254 India non-atheist 2012
## 22255 India non-atheist 2012
## 22256 India non-atheist 2012
## 22257 India non-atheist 2012
## 22258 India non-atheist 2012
## 22259 India non-atheist 2012
## 22260 India non-atheist 2012
## 22261 India non-atheist 2012
## 22262 India non-atheist 2012
## 22263 India non-atheist 2012
## 22264 India non-atheist 2012
## 22265 India non-atheist 2012
## 22266 India non-atheist 2012
## 22267 India non-atheist 2012
## 22268 India non-atheist 2012
## 22269 India non-atheist 2012
## 22270 India non-atheist 2012
## 22271 India non-atheist 2012
## 22272 India non-atheist 2012
## 22273 India non-atheist 2012
## 22274 India non-atheist 2012
## 22275 India non-atheist 2012
## 22276 India non-atheist 2012
## 22277 India atheist 2012
## 22278 India non-atheist 2012
## 22279 India non-atheist 2012
## 22280 India non-atheist 2012
## 22281 India non-atheist 2012
## 22282 India non-atheist 2012
## 22283 India non-atheist 2012
## 22284 India non-atheist 2012
## 22285 India non-atheist 2012
## 22286 India non-atheist 2012
## 22287 India non-atheist 2012
## 22288 India non-atheist 2012
## 22289 India non-atheist 2012
## 22290 India non-atheist 2012
## 22291 India non-atheist 2012
## 22292 India non-atheist 2012
## 22293 India non-atheist 2012
## 22294 India non-atheist 2012
## 22295 India non-atheist 2012
## 22296 India non-atheist 2012
## 22297 India non-atheist 2012
## 22298 India non-atheist 2012
## 22299 India non-atheist 2012
## 22300 India non-atheist 2012
## 22301 India non-atheist 2012
## 22302 India non-atheist 2012
## 22303 India non-atheist 2012
## 22304 India non-atheist 2012
## 22305 India non-atheist 2012
## 22306 India non-atheist 2012
## 22307 India non-atheist 2012
## 22308 India non-atheist 2012
## 22309 India non-atheist 2012
## 22310 India non-atheist 2012
## 22311 India non-atheist 2012
## 22312 India non-atheist 2012
## 22313 India non-atheist 2012
## 22314 India non-atheist 2012
## 22315 India non-atheist 2012
## 22316 India non-atheist 2012
## 22317 India non-atheist 2012
## 22318 India non-atheist 2012
## 22319 India non-atheist 2012
## 22320 India non-atheist 2012
## 22321 India non-atheist 2012
## 22322 India non-atheist 2012
## 22323 India non-atheist 2012
## 22324 India non-atheist 2012
## 22325 India non-atheist 2012
## 22326 India non-atheist 2012
## 22327 India non-atheist 2012
## 22328 India non-atheist 2012
## 22329 India non-atheist 2012
## 22330 India non-atheist 2012
## 22331 India non-atheist 2012
## 22332 India non-atheist 2012
## 22333 India non-atheist 2012
## 22334 India non-atheist 2012
## 22335 India non-atheist 2012
## 22336 India non-atheist 2012
## 22337 India non-atheist 2012
## 22338 India atheist 2012
## 22339 India non-atheist 2012
## 22340 India non-atheist 2012
## 22341 India non-atheist 2012
## 22342 India non-atheist 2012
## 22343 India non-atheist 2012
## 22344 India non-atheist 2012
## 22345 India non-atheist 2012
## 22346 India non-atheist 2012
## 22347 India non-atheist 2012
## 22348 India non-atheist 2012
## 22349 India non-atheist 2012
## 22350 India atheist 2012
## 22351 India non-atheist 2012
## 22352 India non-atheist 2012
## 22353 India non-atheist 2012
## 22354 India non-atheist 2012
## 22355 India non-atheist 2012
## 22356 India non-atheist 2012
## 22357 India non-atheist 2012
## 22358 India non-atheist 2012
## 22359 India non-atheist 2012
## 22360 India non-atheist 2012
## 22361 India non-atheist 2012
## 22362 India non-atheist 2012
## 22363 India non-atheist 2012
## 22364 India non-atheist 2012
## 22365 India non-atheist 2012
## 22366 India non-atheist 2012
## 22367 India non-atheist 2012
## 22368 India non-atheist 2012
## 22369 India non-atheist 2012
## 22370 India non-atheist 2012
## 22371 India non-atheist 2012
## 22372 India non-atheist 2012
## 22373 India non-atheist 2012
## 22374 India non-atheist 2012
## 22375 India non-atheist 2012
## 22376 India non-atheist 2012
## 22377 India non-atheist 2012
## 22378 India non-atheist 2012
## 22379 India non-atheist 2012
## 22380 India non-atheist 2012
## 22381 India non-atheist 2012
## 22382 India non-atheist 2012
## 22383 India non-atheist 2012
## 22384 India non-atheist 2012
## 22385 India non-atheist 2012
## 22386 India non-atheist 2012
## 22387 India non-atheist 2012
## 22388 India non-atheist 2012
## 22389 India atheist 2012
## 22390 India non-atheist 2012
## 22391 India non-atheist 2012
## 22392 India non-atheist 2012
## 22393 India non-atheist 2012
## 22394 India non-atheist 2012
## 22395 India non-atheist 2012
## 22396 India non-atheist 2012
## 22397 India non-atheist 2012
## 22398 India non-atheist 2012
## 22399 India non-atheist 2012
## 22400 India non-atheist 2012
## 22401 India non-atheist 2012
## 22402 India non-atheist 2012
## 22403 India non-atheist 2012
## 22404 India atheist 2012
## 22405 India non-atheist 2012
## 22406 India non-atheist 2012
## 22407 India non-atheist 2012
## 22408 India non-atheist 2012
## 22409 India non-atheist 2012
## 22410 India non-atheist 2012
## 22411 India non-atheist 2012
## 22412 India non-atheist 2012
## 22413 India non-atheist 2012
## 22414 India non-atheist 2012
## 22415 India non-atheist 2012
## 22416 India non-atheist 2012
## 22417 India non-atheist 2012
## 22418 India non-atheist 2012
## 22419 India non-atheist 2012
## 22420 India non-atheist 2012
## 22421 India non-atheist 2012
## 22422 India non-atheist 2012
## 22423 India non-atheist 2012
## 22424 India non-atheist 2012
## 22425 India non-atheist 2012
## 22426 India non-atheist 2012
## 22427 India non-atheist 2012
## 22428 India non-atheist 2012
## 22429 India non-atheist 2012
## 22430 India non-atheist 2012
## 22431 India atheist 2012
## 22432 India non-atheist 2012
## 22433 India non-atheist 2012
## 22434 India non-atheist 2012
## 22435 India non-atheist 2012
## 22436 India non-atheist 2012
## 22437 India non-atheist 2012
## 22438 India non-atheist 2012
## 22439 India non-atheist 2012
## 22440 India non-atheist 2012
## 22441 India non-atheist 2012
## 22442 India non-atheist 2012
## 22443 India atheist 2012
## 22444 India non-atheist 2012
## 22445 India non-atheist 2012
## 22446 India non-atheist 2012
## 22447 India non-atheist 2012
## 22448 India non-atheist 2012
## 22449 India non-atheist 2012
## 22450 India non-atheist 2012
## 22451 India non-atheist 2012
## 22452 India non-atheist 2012
## 22453 India non-atheist 2012
## 22454 India non-atheist 2012
## 22455 India non-atheist 2012
## 22456 India non-atheist 2012
## 22457 India non-atheist 2012
## 22458 India non-atheist 2012
## 22459 India non-atheist 2012
## 22460 India non-atheist 2012
## 22461 India non-atheist 2012
## 22462 India non-atheist 2012
## 22463 India non-atheist 2012
## 22464 India non-atheist 2012
## 22465 India non-atheist 2012
## 22466 India non-atheist 2012
## 22467 India non-atheist 2012
## 22468 India non-atheist 2012
## 22469 India non-atheist 2012
## 22470 India non-atheist 2012
## 22471 India non-atheist 2012
## 22472 India non-atheist 2012
## 22473 India non-atheist 2012
## 22474 India non-atheist 2012
## 22475 India non-atheist 2012
## 22476 India non-atheist 2012
## 22477 India non-atheist 2012
## 22478 India non-atheist 2012
## 22479 India non-atheist 2012
## 22480 India non-atheist 2012
## 22481 India non-atheist 2012
## 22482 India non-atheist 2012
## 22483 India non-atheist 2012
## 22484 India non-atheist 2012
## 22485 India non-atheist 2012
## 22486 India non-atheist 2012
## 22487 India non-atheist 2012
## 22488 India non-atheist 2012
## 22489 India non-atheist 2012
## 22490 India non-atheist 2012
## 22491 India non-atheist 2012
## 22492 India non-atheist 2012
## 22493 India non-atheist 2012
## 22494 India non-atheist 2012
## 22495 India non-atheist 2012
## 22496 India non-atheist 2012
## 22497 India non-atheist 2012
## 22498 India non-atheist 2012
## 22499 India non-atheist 2012
## 22500 India non-atheist 2012
## 22501 India non-atheist 2012
## 22502 India non-atheist 2012
## 22503 India non-atheist 2012
## 22504 India non-atheist 2012
## 22505 India non-atheist 2012
## 22506 India non-atheist 2012
## 22507 India non-atheist 2012
## 22508 India non-atheist 2012
## 22509 India non-atheist 2012
## 22510 India non-atheist 2012
## 22511 India non-atheist 2012
## 22512 India non-atheist 2012
## 22513 India non-atheist 2012
## 22514 India non-atheist 2012
## 22515 India non-atheist 2012
## 22516 India non-atheist 2012
## 22517 India non-atheist 2012
## 22518 India non-atheist 2012
## 22519 India non-atheist 2012
## 22520 India non-atheist 2012
## 22521 India non-atheist 2012
## 22522 India non-atheist 2012
## 22523 India non-atheist 2012
## 22524 India non-atheist 2012
## 22525 India non-atheist 2012
## 22526 India non-atheist 2012
## 22527 India non-atheist 2012
## 22528 India non-atheist 2012
## 22529 India non-atheist 2012
## 22530 India non-atheist 2012
## 22531 India non-atheist 2012
## 22532 India atheist 2012
## 22533 India non-atheist 2012
## 22534 India non-atheist 2012
## 22535 India non-atheist 2012
## 22536 India non-atheist 2012
## 22537 India non-atheist 2012
## 22538 India non-atheist 2012
## 22539 India non-atheist 2012
## 22540 India non-atheist 2012
## 22541 India non-atheist 2012
## 22542 India non-atheist 2012
## 22543 India non-atheist 2012
## 22544 India non-atheist 2012
## 22545 India non-atheist 2012
## 22546 India non-atheist 2012
## 22547 India non-atheist 2012
## 22548 India non-atheist 2012
## 22549 India non-atheist 2012
## 22550 India non-atheist 2012
## 22551 India non-atheist 2012
## 22552 India non-atheist 2012
## 22553 India non-atheist 2012
## 22554 India non-atheist 2012
## 22555 India non-atheist 2012
## 22556 India non-atheist 2012
## 22557 India non-atheist 2012
## 22558 India non-atheist 2012
## 22559 India non-atheist 2012
## 22560 India non-atheist 2012
## 22561 India non-atheist 2012
## 22562 India non-atheist 2012
## 22563 India non-atheist 2012
## 22564 India non-atheist 2012
## 22565 India non-atheist 2012
## 22566 India non-atheist 2012
## 22567 India non-atheist 2012
## 22568 India non-atheist 2012
## 22569 India non-atheist 2012
## 22570 India non-atheist 2012
## 22571 India non-atheist 2012
## 22572 India non-atheist 2012
## 22573 India non-atheist 2012
## 22574 India non-atheist 2012
## 22575 India non-atheist 2012
## 22576 India non-atheist 2012
## 22577 India non-atheist 2012
## 22578 India non-atheist 2012
## 22579 India non-atheist 2012
## 22580 India non-atheist 2012
## 22581 India non-atheist 2012
## 22582 India non-atheist 2012
## 22583 India non-atheist 2012
## 22584 India non-atheist 2012
## 22585 India non-atheist 2012
## 22586 India non-atheist 2012
## 22587 India non-atheist 2012
## 22588 India non-atheist 2012
## 22589 India non-atheist 2012
## 22590 India non-atheist 2012
## 22591 India non-atheist 2012
## 22592 India non-atheist 2012
## 22593 India non-atheist 2012
## 22594 India non-atheist 2012
## 22595 India non-atheist 2012
## 22596 India non-atheist 2012
## 22597 India non-atheist 2012
## 22598 India non-atheist 2012
## 22599 India non-atheist 2012
## 22600 India non-atheist 2012
## 22601 India non-atheist 2012
## 22602 India non-atheist 2012
## 22603 India non-atheist 2012
## 22604 India non-atheist 2012
## 22605 India non-atheist 2012
## 22606 India non-atheist 2012
## 22607 India non-atheist 2012
## 22608 India non-atheist 2012
## 22609 India non-atheist 2012
## 22610 India non-atheist 2012
## 22611 India atheist 2012
## 22612 India non-atheist 2012
## 22613 India non-atheist 2012
## 22614 India non-atheist 2012
## 22615 India non-atheist 2012
## 22616 India non-atheist 2012
## 22617 India non-atheist 2012
## 22618 India non-atheist 2012
## 22619 India non-atheist 2012
## 22620 India non-atheist 2012
## 22621 India non-atheist 2012
## 22622 India non-atheist 2012
## 22623 India non-atheist 2012
## 22624 India non-atheist 2012
## 22625 India non-atheist 2012
## 22626 India non-atheist 2012
## 22627 India non-atheist 2012
## 22628 India non-atheist 2012
## 22629 India non-atheist 2012
## 22630 India non-atheist 2012
## 22631 India non-atheist 2012
## 22632 India non-atheist 2012
## 22633 India non-atheist 2012
## 22634 India non-atheist 2012
## 22635 India non-atheist 2012
## 22636 India non-atheist 2012
## 22637 India non-atheist 2012
## 22638 India non-atheist 2012
## 22639 India non-atheist 2012
## 22640 India non-atheist 2012
## 22641 India non-atheist 2012
## 22642 India non-atheist 2012
## 22643 India non-atheist 2012
## 22644 India non-atheist 2012
## 22645 India non-atheist 2012
## 22646 India non-atheist 2012
## 22647 India non-atheist 2012
## 22648 India non-atheist 2012
## 22649 India non-atheist 2012
## 22650 India non-atheist 2012
## 22651 India non-atheist 2012
## 22652 India non-atheist 2012
## 22653 India non-atheist 2012
## 22654 India non-atheist 2012
## 22655 India atheist 2012
## 22656 India non-atheist 2012
## 22657 India non-atheist 2012
## 22658 India non-atheist 2012
## 22659 India non-atheist 2012
## 22660 India non-atheist 2012
## 22661 India non-atheist 2012
## 22662 India non-atheist 2012
## 22663 India non-atheist 2012
## 22664 India non-atheist 2012
## 22665 India non-atheist 2012
## 22666 India non-atheist 2012
## 22667 India non-atheist 2012
## 22668 India non-atheist 2012
## 22669 India non-atheist 2012
## 22670 India non-atheist 2012
## 22671 India non-atheist 2012
## 22672 India non-atheist 2012
## 22673 India non-atheist 2012
## 22674 India non-atheist 2012
## 22675 India non-atheist 2012
## 22676 India non-atheist 2012
## 22677 India non-atheist 2012
## 22678 India non-atheist 2012
## 22679 India non-atheist 2012
## 22680 India non-atheist 2012
## 22681 India non-atheist 2012
## 22682 India non-atheist 2012
## 22683 India non-atheist 2012
## 22684 India non-atheist 2012
## 22685 India atheist 2012
## 22686 India non-atheist 2012
## 22687 India non-atheist 2012
## 22688 India non-atheist 2012
## 22689 India non-atheist 2012
## 22690 India non-atheist 2012
## 22691 India atheist 2012
## 22692 India non-atheist 2012
## 22693 India non-atheist 2012
## 22694 India non-atheist 2012
## 22695 India non-atheist 2012
## 22696 India non-atheist 2012
## 22697 India non-atheist 2012
## 22698 India non-atheist 2012
## 22699 India non-atheist 2012
## 22700 India non-atheist 2012
## 22701 India non-atheist 2012
## 22702 India non-atheist 2012
## 22703 India non-atheist 2012
## 22704 India non-atheist 2012
## 22705 India non-atheist 2012
## 22706 India non-atheist 2012
## 22707 India non-atheist 2012
## 22708 India non-atheist 2012
## 22709 India non-atheist 2012
## 22710 India non-atheist 2012
## 22711 India non-atheist 2012
## 22712 India non-atheist 2012
## 22713 India non-atheist 2012
## 22714 India non-atheist 2012
## 22715 India non-atheist 2012
## 22716 India non-atheist 2012
## 22717 India non-atheist 2012
## 22718 India non-atheist 2012
## 22719 India non-atheist 2012
## 22720 India non-atheist 2012
## 22721 India non-atheist 2012
## 22722 India non-atheist 2012
## 22723 India non-atheist 2012
## 22724 India non-atheist 2012
## 22725 India non-atheist 2012
## 22726 India non-atheist 2012
## 22727 India non-atheist 2012
## 22728 India non-atheist 2012
## 22729 India non-atheist 2012
## 22730 India non-atheist 2012
## 22731 India non-atheist 2012
## 22732 India non-atheist 2012
## 22733 India non-atheist 2012
## 22734 India non-atheist 2012
## 22735 India non-atheist 2012
## 22736 India non-atheist 2012
## 22737 India non-atheist 2012
## 22738 India non-atheist 2012
## 22739 India non-atheist 2012
## 22740 India non-atheist 2012
## 22741 India non-atheist 2012
## 22742 India non-atheist 2012
## 22743 India non-atheist 2012
## 22744 India non-atheist 2012
## 22745 India non-atheist 2012inference(in12$response, est = "proportion", type = "ci", method = "theoretical",
success = "atheist")## Single proportion -- success: atheist
## Summary statistics:
## p_hat = 0.0302 ; n = 1092
## Check conditions: number of successes = 33 ; number of failures = 1059
## Standard error = 0.0052
## 95 % Confidence interval = ( 0.0201 , 0.0404 )jp12 <- subset(atheism, nationality == "Japan" & year == "2012")
jp12## nationality response year
## 25743 Japan non-atheist 2012
## 25744 Japan atheist 2012
## 25745 Japan atheist 2012
## 25746 Japan non-atheist 2012
## 25747 Japan atheist 2012
## 25748 Japan non-atheist 2012
## 25749 Japan non-atheist 2012
## 25750 Japan non-atheist 2012
## 25751 Japan non-atheist 2012
## 25752 Japan atheist 2012
## 25753 Japan atheist 2012
## 25754 Japan non-atheist 2012
## 25755 Japan non-atheist 2012
## 25756 Japan non-atheist 2012
## 25757 Japan non-atheist 2012
## 25758 Japan non-atheist 2012
## 25759 Japan atheist 2012
## 25760 Japan atheist 2012
## 25761 Japan atheist 2012
## 25762 Japan atheist 2012
## 25763 Japan atheist 2012
## 25764 Japan atheist 2012
## 25765 Japan non-atheist 2012
## 25766 Japan non-atheist 2012
## 25767 Japan non-atheist 2012
## 25768 Japan non-atheist 2012
## 25769 Japan non-atheist 2012
## 25770 Japan atheist 2012
## 25771 Japan atheist 2012
## 25772 Japan non-atheist 2012
## 25773 Japan non-atheist 2012
## 25774 Japan atheist 2012
## 25775 Japan non-atheist 2012
## 25776 Japan non-atheist 2012
## 25777 Japan non-atheist 2012
## 25778 Japan atheist 2012
## 25779 Japan non-atheist 2012
## 25780 Japan non-atheist 2012
## 25781 Japan non-atheist 2012
## 25782 Japan atheist 2012
## 25783 Japan non-atheist 2012
## 25784 Japan non-atheist 2012
## 25785 Japan non-atheist 2012
## 25786 Japan non-atheist 2012
## 25787 Japan non-atheist 2012
## 25788 Japan non-atheist 2012
## 25789 Japan atheist 2012
## 25790 Japan non-atheist 2012
## 25791 Japan non-atheist 2012
## 25792 Japan non-atheist 2012
## 25793 Japan non-atheist 2012
## 25794 Japan non-atheist 2012
## 25795 Japan non-atheist 2012
## 25796 Japan atheist 2012
## 25797 Japan atheist 2012
## 25798 Japan non-atheist 2012
## 25799 Japan non-atheist 2012
## 25800 Japan atheist 2012
## 25801 Japan atheist 2012
## 25802 Japan non-atheist 2012
## 25803 Japan non-atheist 2012
## 25804 Japan atheist 2012
## 25805 Japan non-atheist 2012
## 25806 Japan non-atheist 2012
## 25807 Japan non-atheist 2012
## 25808 Japan atheist 2012
## 25809 Japan non-atheist 2012
## 25810 Japan non-atheist 2012
## 25811 Japan atheist 2012
## 25812 Japan non-atheist 2012
## 25813 Japan non-atheist 2012
## 25814 Japan non-atheist 2012
## 25815 Japan atheist 2012
## 25816 Japan non-atheist 2012
## 25817 Japan non-atheist 2012
## 25818 Japan non-atheist 2012
## 25819 Japan non-atheist 2012
## 25820 Japan non-atheist 2012
## 25821 Japan non-atheist 2012
## 25822 Japan non-atheist 2012
## 25823 Japan non-atheist 2012
## 25824 Japan non-atheist 2012
## 25825 Japan non-atheist 2012
## 25826 Japan atheist 2012
## 25827 Japan non-atheist 2012
## 25828 Japan non-atheist 2012
## 25829 Japan atheist 2012
## 25830 Japan non-atheist 2012
## 25831 Japan non-atheist 2012
## 25832 Japan atheist 2012
## 25833 Japan atheist 2012
## 25834 Japan non-atheist 2012
## 25835 Japan non-atheist 2012
## 25836 Japan non-atheist 2012
## 25837 Japan non-atheist 2012
## 25838 Japan non-atheist 2012
## 25839 Japan non-atheist 2012
## 25840 Japan atheist 2012
## 25841 Japan non-atheist 2012
## 25842 Japan atheist 2012
## 25843 Japan non-atheist 2012
## 25844 Japan atheist 2012
## 25845 Japan non-atheist 2012
## 25846 Japan atheist 2012
## 25847 Japan non-atheist 2012
## 25848 Japan non-atheist 2012
## 25849 Japan non-atheist 2012
## 25850 Japan non-atheist 2012
## 25851 Japan non-atheist 2012
## 25852 Japan non-atheist 2012
## 25853 Japan atheist 2012
## 25854 Japan atheist 2012
## 25855 Japan non-atheist 2012
## 25856 Japan non-atheist 2012
## 25857 Japan non-atheist 2012
## 25858 Japan non-atheist 2012
## 25859 Japan non-atheist 2012
## 25860 Japan non-atheist 2012
## 25861 Japan non-atheist 2012
## 25862 Japan atheist 2012
## 25863 Japan non-atheist 2012
## 25864 Japan atheist 2012
## 25865 Japan non-atheist 2012
## 25866 Japan non-atheist 2012
## 25867 Japan atheist 2012
## 25868 Japan atheist 2012
## 25869 Japan non-atheist 2012
## 25870 Japan atheist 2012
## 25871 Japan atheist 2012
## 25872 Japan atheist 2012
## 25873 Japan atheist 2012
## 25874 Japan atheist 2012
## 25875 Japan non-atheist 2012
## 25876 Japan atheist 2012
## 25877 Japan atheist 2012
## 25878 Japan atheist 2012
## 25879 Japan non-atheist 2012
## 25880 Japan atheist 2012
## 25881 Japan non-atheist 2012
## 25882 Japan non-atheist 2012
## 25883 Japan non-atheist 2012
## 25884 Japan non-atheist 2012
## 25885 Japan non-atheist 2012
## 25886 Japan atheist 2012
## 25887 Japan non-atheist 2012
## 25888 Japan non-atheist 2012
## 25889 Japan non-atheist 2012
## 25890 Japan non-atheist 2012
## 25891 Japan atheist 2012
## 25892 Japan non-atheist 2012
## 25893 Japan non-atheist 2012
## 25894 Japan non-atheist 2012
## 25895 Japan atheist 2012
## 25896 Japan non-atheist 2012
## 25897 Japan non-atheist 2012
## 25898 Japan non-atheist 2012
## 25899 Japan non-atheist 2012
## 25900 Japan non-atheist 2012
## 25901 Japan atheist 2012
## 25902 Japan non-atheist 2012
## 25903 Japan non-atheist 2012
## 25904 Japan atheist 2012
## 25905 Japan non-atheist 2012
## 25906 Japan atheist 2012
## 25907 Japan non-atheist 2012
## 25908 Japan non-atheist 2012
## 25909 Japan atheist 2012
## 25910 Japan non-atheist 2012
## 25911 Japan atheist 2012
## 25912 Japan non-atheist 2012
## 25913 Japan non-atheist 2012
## 25914 Japan atheist 2012
## 25915 Japan atheist 2012
## 25916 Japan non-atheist 2012
## 25917 Japan atheist 2012
## 25918 Japan non-atheist 2012
## 25919 Japan atheist 2012
## 25920 Japan non-atheist 2012
## 25921 Japan non-atheist 2012
## 25922 Japan non-atheist 2012
## 25923 Japan non-atheist 2012
## 25924 Japan non-atheist 2012
## 25925 Japan non-atheist 2012
## 25926 Japan atheist 2012
## 25927 Japan non-atheist 2012
## 25928 Japan atheist 2012
## 25929 Japan non-atheist 2012
## 25930 Japan non-atheist 2012
## 25931 Japan atheist 2012
## 25932 Japan non-atheist 2012
## 25933 Japan non-atheist 2012
## 25934 Japan non-atheist 2012
## 25935 Japan atheist 2012
## 25936 Japan atheist 2012
## 25937 Japan atheist 2012
## 25938 Japan non-atheist 2012
## 25939 Japan non-atheist 2012
## 25940 Japan atheist 2012
## 25941 Japan non-atheist 2012
## 25942 Japan non-atheist 2012
## 25943 Japan non-atheist 2012
## 25944 Japan atheist 2012
## 25945 Japan non-atheist 2012
## 25946 Japan atheist 2012
## 25947 Japan atheist 2012
## 25948 Japan non-atheist 2012
## 25949 Japan non-atheist 2012
## 25950 Japan non-atheist 2012
## 25951 Japan non-atheist 2012
## 25952 Japan non-atheist 2012
## 25953 Japan non-atheist 2012
## 25954 Japan non-atheist 2012
## 25955 Japan non-atheist 2012
## 25956 Japan atheist 2012
## 25957 Japan non-atheist 2012
## 25958 Japan non-atheist 2012
## 25959 Japan non-atheist 2012
## 25960 Japan atheist 2012
## 25961 Japan non-atheist 2012
## 25962 Japan non-atheist 2012
## 25963 Japan non-atheist 2012
## 25964 Japan atheist 2012
## 25965 Japan atheist 2012
## 25966 Japan atheist 2012
## 25967 Japan non-atheist 2012
## 25968 Japan non-atheist 2012
## 25969 Japan non-atheist 2012
## 25970 Japan non-atheist 2012
## 25971 Japan non-atheist 2012
## 25972 Japan non-atheist 2012
## 25973 Japan non-atheist 2012
## 25974 Japan non-atheist 2012
## 25975 Japan non-atheist 2012
## 25976 Japan non-atheist 2012
## 25977 Japan non-atheist 2012
## 25978 Japan non-atheist 2012
## 25979 Japan non-atheist 2012
## 25980 Japan atheist 2012
## 25981 Japan non-atheist 2012
## 25982 Japan non-atheist 2012
## 25983 Japan non-atheist 2012
## 25984 Japan atheist 2012
## 25985 Japan non-atheist 2012
## 25986 Japan non-atheist 2012
## 25987 Japan atheist 2012
## 25988 Japan non-atheist 2012
## 25989 Japan non-atheist 2012
## 25990 Japan atheist 2012
## 25991 Japan non-atheist 2012
## 25992 Japan non-atheist 2012
## 25993 Japan non-atheist 2012
## 25994 Japan atheist 2012
## 25995 Japan non-atheist 2012
## 25996 Japan atheist 2012
## 25997 Japan non-atheist 2012
## 25998 Japan non-atheist 2012
## 25999 Japan non-atheist 2012
## 26000 Japan non-atheist 2012
## 26001 Japan non-atheist 2012
## 26002 Japan non-atheist 2012
## 26003 Japan non-atheist 2012
## 26004 Japan non-atheist 2012
## 26005 Japan atheist 2012
## 26006 Japan non-atheist 2012
## 26007 Japan non-atheist 2012
## 26008 Japan non-atheist 2012
## 26009 Japan atheist 2012
## 26010 Japan non-atheist 2012
## 26011 Japan atheist 2012
## 26012 Japan non-atheist 2012
## 26013 Japan atheist 2012
## 26014 Japan non-atheist 2012
## 26015 Japan non-atheist 2012
## 26016 Japan non-atheist 2012
## 26017 Japan non-atheist 2012
## 26018 Japan non-atheist 2012
## 26019 Japan non-atheist 2012
## 26020 Japan atheist 2012
## 26021 Japan non-atheist 2012
## 26022 Japan non-atheist 2012
## 26023 Japan non-atheist 2012
## 26024 Japan non-atheist 2012
## 26025 Japan atheist 2012
## 26026 Japan non-atheist 2012
## 26027 Japan atheist 2012
## 26028 Japan non-atheist 2012
## 26029 Japan non-atheist 2012
## 26030 Japan non-atheist 2012
## 26031 Japan non-atheist 2012
## 26032 Japan non-atheist 2012
## 26033 Japan non-atheist 2012
## 26034 Japan non-atheist 2012
## 26035 Japan non-atheist 2012
## 26036 Japan non-atheist 2012
## 26037 Japan non-atheist 2012
## 26038 Japan non-atheist 2012
## 26039 Japan atheist 2012
## 26040 Japan non-atheist 2012
## 26041 Japan atheist 2012
## 26042 Japan non-atheist 2012
## 26043 Japan non-atheist 2012
## 26044 Japan non-atheist 2012
## 26045 Japan atheist 2012
## 26046 Japan non-atheist 2012
## 26047 Japan non-atheist 2012
## 26048 Japan non-atheist 2012
## 26049 Japan non-atheist 2012
## 26050 Japan non-atheist 2012
## 26051 Japan atheist 2012
## 26052 Japan atheist 2012
## 26053 Japan non-atheist 2012
## 26054 Japan non-atheist 2012
## 26055 Japan non-atheist 2012
## 26056 Japan non-atheist 2012
## 26057 Japan non-atheist 2012
## 26058 Japan non-atheist 2012
## 26059 Japan non-atheist 2012
## 26060 Japan non-atheist 2012
## 26061 Japan non-atheist 2012
## 26062 Japan non-atheist 2012
## 26063 Japan non-atheist 2012
## 26064 Japan non-atheist 2012
## 26065 Japan atheist 2012
## 26066 Japan non-atheist 2012
## 26067 Japan non-atheist 2012
## 26068 Japan non-atheist 2012
## 26069 Japan non-atheist 2012
## 26070 Japan non-atheist 2012
## 26071 Japan atheist 2012
## 26072 Japan atheist 2012
## 26073 Japan non-atheist 2012
## 26074 Japan atheist 2012
## 26075 Japan atheist 2012
## 26076 Japan non-atheist 2012
## 26077 Japan non-atheist 2012
## 26078 Japan non-atheist 2012
## 26079 Japan non-atheist 2012
## 26080 Japan non-atheist 2012
## 26081 Japan non-atheist 2012
## 26082 Japan atheist 2012
## 26083 Japan non-atheist 2012
## 26084 Japan non-atheist 2012
## 26085 Japan atheist 2012
## 26086 Japan non-atheist 2012
## 26087 Japan non-atheist 2012
## 26088 Japan non-atheist 2012
## 26089 Japan atheist 2012
## 26090 Japan non-atheist 2012
## 26091 Japan non-atheist 2012
## 26092 Japan non-atheist 2012
## 26093 Japan non-atheist 2012
## 26094 Japan atheist 2012
## 26095 Japan atheist 2012
## 26096 Japan non-atheist 2012
## 26097 Japan atheist 2012
## 26098 Japan non-atheist 2012
## 26099 Japan non-atheist 2012
## 26100 Japan non-atheist 2012
## 26101 Japan non-atheist 2012
## 26102 Japan atheist 2012
## 26103 Japan atheist 2012
## 26104 Japan atheist 2012
## 26105 Japan non-atheist 2012
## 26106 Japan atheist 2012
## 26107 Japan atheist 2012
## 26108 Japan atheist 2012
## 26109 Japan atheist 2012
## 26110 Japan atheist 2012
## 26111 Japan non-atheist 2012
## 26112 Japan non-atheist 2012
## 26113 Japan non-atheist 2012
## 26114 Japan atheist 2012
## 26115 Japan non-atheist 2012
## 26116 Japan non-atheist 2012
## 26117 Japan non-atheist 2012
## 26118 Japan non-atheist 2012
## 26119 Japan non-atheist 2012
## 26120 Japan non-atheist 2012
## 26121 Japan non-atheist 2012
## 26122 Japan atheist 2012
## 26123 Japan non-atheist 2012
## 26124 Japan non-atheist 2012
## 26125 Japan non-atheist 2012
## 26126 Japan non-atheist 2012
## 26127 Japan atheist 2012
## 26128 Japan non-atheist 2012
## 26129 Japan non-atheist 2012
## 26130 Japan non-atheist 2012
## 26131 Japan non-atheist 2012
## 26132 Japan non-atheist 2012
## 26133 Japan non-atheist 2012
## 26134 Japan non-atheist 2012
## 26135 Japan non-atheist 2012
## 26136 Japan non-atheist 2012
## 26137 Japan non-atheist 2012
## 26138 Japan non-atheist 2012
## 26139 Japan non-atheist 2012
## 26140 Japan non-atheist 2012
## 26141 Japan atheist 2012
## 26142 Japan non-atheist 2012
## 26143 Japan non-atheist 2012
## 26144 Japan non-atheist 2012
## 26145 Japan non-atheist 2012
## 26146 Japan non-atheist 2012
## 26147 Japan atheist 2012
## 26148 Japan non-atheist 2012
## 26149 Japan non-atheist 2012
## 26150 Japan non-atheist 2012
## 26151 Japan atheist 2012
## 26152 Japan non-atheist 2012
## 26153 Japan non-atheist 2012
## 26154 Japan non-atheist 2012
## 26155 Japan non-atheist 2012
## 26156 Japan non-atheist 2012
## 26157 Japan atheist 2012
## 26158 Japan non-atheist 2012
## 26159 Japan non-atheist 2012
## 26160 Japan non-atheist 2012
## 26161 Japan non-atheist 2012
## 26162 Japan non-atheist 2012
## 26163 Japan non-atheist 2012
## 26164 Japan non-atheist 2012
## 26165 Japan non-atheist 2012
## 26166 Japan non-atheist 2012
## 26167 Japan non-atheist 2012
## 26168 Japan non-atheist 2012
## 26169 Japan atheist 2012
## 26170 Japan non-atheist 2012
## 26171 Japan atheist 2012
## 26172 Japan atheist 2012
## 26173 Japan atheist 2012
## 26174 Japan atheist 2012
## 26175 Japan atheist 2012
## 26176 Japan non-atheist 2012
## 26177 Japan atheist 2012
## 26178 Japan non-atheist 2012
## 26179 Japan non-atheist 2012
## 26180 Japan non-atheist 2012
## 26181 Japan non-atheist 2012
## 26182 Japan atheist 2012
## 26183 Japan atheist 2012
## 26184 Japan atheist 2012
## 26185 Japan non-atheist 2012
## 26186 Japan non-atheist 2012
## 26187 Japan non-atheist 2012
## 26188 Japan non-atheist 2012
## 26189 Japan atheist 2012
## 26190 Japan atheist 2012
## 26191 Japan atheist 2012
## 26192 Japan non-atheist 2012
## 26193 Japan atheist 2012
## 26194 Japan non-atheist 2012
## 26195 Japan atheist 2012
## 26196 Japan atheist 2012
## 26197 Japan atheist 2012
## 26198 Japan non-atheist 2012
## 26199 Japan non-atheist 2012
## 26200 Japan non-atheist 2012
## 26201 Japan atheist 2012
## 26202 Japan atheist 2012
## 26203 Japan atheist 2012
## 26204 Japan non-atheist 2012
## 26205 Japan non-atheist 2012
## 26206 Japan non-atheist 2012
## 26207 Japan non-atheist 2012
## 26208 Japan non-atheist 2012
## 26209 Japan non-atheist 2012
## 26210 Japan atheist 2012
## 26211 Japan non-atheist 2012
## 26212 Japan atheist 2012
## 26213 Japan atheist 2012
## 26214 Japan non-atheist 2012
## 26215 Japan atheist 2012
## 26216 Japan atheist 2012
## 26217 Japan atheist 2012
## 26218 Japan atheist 2012
## 26219 Japan atheist 2012
## 26220 Japan non-atheist 2012
## 26221 Japan non-atheist 2012
## 26222 Japan non-atheist 2012
## 26223 Japan non-atheist 2012
## 26224 Japan non-atheist 2012
## 26225 Japan atheist 2012
## 26226 Japan atheist 2012
## 26227 Japan non-atheist 2012
## 26228 Japan atheist 2012
## 26229 Japan non-atheist 2012
## 26230 Japan non-atheist 2012
## 26231 Japan non-atheist 2012
## 26232 Japan non-atheist 2012
## 26233 Japan non-atheist 2012
## 26234 Japan atheist 2012
## 26235 Japan non-atheist 2012
## 26236 Japan atheist 2012
## 26237 Japan non-atheist 2012
## 26238 Japan atheist 2012
## 26239 Japan atheist 2012
## 26240 Japan non-atheist 2012
## 26241 Japan non-atheist 2012
## 26242 Japan non-atheist 2012
## 26243 Japan non-atheist 2012
## 26244 Japan non-atheist 2012
## 26245 Japan non-atheist 2012
## 26246 Japan non-atheist 2012
## 26247 Japan non-atheist 2012
## 26248 Japan non-atheist 2012
## 26249 Japan non-atheist 2012
## 26250 Japan non-atheist 2012
## 26251 Japan non-atheist 2012
## 26252 Japan non-atheist 2012
## 26253 Japan non-atheist 2012
## 26254 Japan non-atheist 2012
## 26255 Japan atheist 2012
## 26256 Japan non-atheist 2012
## 26257 Japan non-atheist 2012
## 26258 Japan atheist 2012
## 26259 Japan non-atheist 2012
## 26260 Japan non-atheist 2012
## 26261 Japan atheist 2012
## 26262 Japan atheist 2012
## 26263 Japan non-atheist 2012
## 26264 Japan atheist 2012
## 26265 Japan atheist 2012
## 26266 Japan non-atheist 2012
## 26267 Japan non-atheist 2012
## 26268 Japan non-atheist 2012
## 26269 Japan non-atheist 2012
## 26270 Japan non-atheist 2012
## 26271 Japan non-atheist 2012
## 26272 Japan non-atheist 2012
## 26273 Japan non-atheist 2012
## 26274 Japan non-atheist 2012
## 26275 Japan non-atheist 2012
## 26276 Japan non-atheist 2012
## 26277 Japan atheist 2012
## 26278 Japan non-atheist 2012
## 26279 Japan non-atheist 2012
## 26280 Japan non-atheist 2012
## 26281 Japan non-atheist 2012
## 26282 Japan non-atheist 2012
## 26283 Japan non-atheist 2012
## 26284 Japan non-atheist 2012
## 26285 Japan non-atheist 2012
## 26286 Japan non-atheist 2012
## 26287 Japan atheist 2012
## 26288 Japan non-atheist 2012
## 26289 Japan non-atheist 2012
## 26290 Japan atheist 2012
## 26291 Japan non-atheist 2012
## 26292 Japan non-atheist 2012
## 26293 Japan non-atheist 2012
## 26294 Japan atheist 2012
## 26295 Japan non-atheist 2012
## 26296 Japan atheist 2012
## 26297 Japan non-atheist 2012
## 26298 Japan non-atheist 2012
## 26299 Japan non-atheist 2012
## 26300 Japan non-atheist 2012
## 26301 Japan atheist 2012
## 26302 Japan non-atheist 2012
## 26303 Japan atheist 2012
## 26304 Japan non-atheist 2012
## 26305 Japan non-atheist 2012
## 26306 Japan non-atheist 2012
## 26307 Japan atheist 2012
## 26308 Japan non-atheist 2012
## 26309 Japan non-atheist 2012
## 26310 Japan non-atheist 2012
## 26311 Japan non-atheist 2012
## 26312 Japan non-atheist 2012
## 26313 Japan non-atheist 2012
## 26314 Japan non-atheist 2012
## 26315 Japan non-atheist 2012
## 26316 Japan non-atheist 2012
## 26317 Japan atheist 2012
## 26318 Japan non-atheist 2012
## 26319 Japan atheist 2012
## 26320 Japan non-atheist 2012
## 26321 Japan non-atheist 2012
## 26322 Japan atheist 2012
## 26323 Japan non-atheist 2012
## 26324 Japan non-atheist 2012
## 26325 Japan atheist 2012
## 26326 Japan non-atheist 2012
## 26327 Japan non-atheist 2012
## 26328 Japan non-atheist 2012
## 26329 Japan non-atheist 2012
## 26330 Japan non-atheist 2012
## 26331 Japan atheist 2012
## 26332 Japan non-atheist 2012
## 26333 Japan non-atheist 2012
## 26334 Japan non-atheist 2012
## 26335 Japan atheist 2012
## 26336 Japan non-atheist 2012
## 26337 Japan atheist 2012
## 26338 Japan atheist 2012
## 26339 Japan non-atheist 2012
## 26340 Japan non-atheist 2012
## 26341 Japan non-atheist 2012
## 26342 Japan non-atheist 2012
## 26343 Japan non-atheist 2012
## 26344 Japan non-atheist 2012
## 26345 Japan non-atheist 2012
## 26346 Japan atheist 2012
## 26347 Japan non-atheist 2012
## 26348 Japan non-atheist 2012
## 26349 Japan non-atheist 2012
## 26350 Japan non-atheist 2012
## 26351 Japan non-atheist 2012
## 26352 Japan non-atheist 2012
## 26353 Japan non-atheist 2012
## 26354 Japan atheist 2012
## 26355 Japan non-atheist 2012
## 26356 Japan non-atheist 2012
## 26357 Japan non-atheist 2012
## 26358 Japan non-atheist 2012
## 26359 Japan atheist 2012
## 26360 Japan non-atheist 2012
## 26361 Japan non-atheist 2012
## 26362 Japan non-atheist 2012
## 26363 Japan non-atheist 2012
## 26364 Japan non-atheist 2012
## 26365 Japan non-atheist 2012
## 26366 Japan atheist 2012
## 26367 Japan atheist 2012
## 26368 Japan atheist 2012
## 26369 Japan non-atheist 2012
## 26370 Japan atheist 2012
## 26371 Japan atheist 2012
## 26372 Japan non-atheist 2012
## 26373 Japan non-atheist 2012
## 26374 Japan atheist 2012
## 26375 Japan atheist 2012
## 26376 Japan non-atheist 2012
## 26377 Japan non-atheist 2012
## 26378 Japan atheist 2012
## 26379 Japan atheist 2012
## 26380 Japan atheist 2012
## 26381 Japan non-atheist 2012
## 26382 Japan non-atheist 2012
## 26383 Japan non-atheist 2012
## 26384 Japan non-atheist 2012
## 26385 Japan non-atheist 2012
## 26386 Japan atheist 2012
## 26387 Japan atheist 2012
## 26388 Japan non-atheist 2012
## 26389 Japan atheist 2012
## 26390 Japan non-atheist 2012
## 26391 Japan atheist 2012
## 26392 Japan non-atheist 2012
## 26393 Japan non-atheist 2012
## 26394 Japan non-atheist 2012
## 26395 Japan atheist 2012
## 26396 Japan atheist 2012
## 26397 Japan non-atheist 2012
## 26398 Japan non-atheist 2012
## 26399 Japan non-atheist 2012
## 26400 Japan non-atheist 2012
## 26401 Japan atheist 2012
## 26402 Japan atheist 2012
## 26403 Japan non-atheist 2012
## 26404 Japan non-atheist 2012
## 26405 Japan non-atheist 2012
## 26406 Japan atheist 2012
## 26407 Japan non-atheist 2012
## 26408 Japan non-atheist 2012
## 26409 Japan non-atheist 2012
## 26410 Japan atheist 2012
## 26411 Japan atheist 2012
## 26412 Japan atheist 2012
## 26413 Japan non-atheist 2012
## 26414 Japan non-atheist 2012
## 26415 Japan non-atheist 2012
## 26416 Japan non-atheist 2012
## 26417 Japan non-atheist 2012
## 26418 Japan atheist 2012
## 26419 Japan non-atheist 2012
## 26420 Japan non-atheist 2012
## 26421 Japan non-atheist 2012
## 26422 Japan non-atheist 2012
## 26423 Japan non-atheist 2012
## 26424 Japan non-atheist 2012
## 26425 Japan atheist 2012
## 26426 Japan non-atheist 2012
## 26427 Japan atheist 2012
## 26428 Japan non-atheist 2012
## 26429 Japan atheist 2012
## 26430 Japan non-atheist 2012
## 26431 Japan non-atheist 2012
## 26432 Japan atheist 2012
## 26433 Japan non-atheist 2012
## 26434 Japan non-atheist 2012
## 26435 Japan non-atheist 2012
## 26436 Japan non-atheist 2012
## 26437 Japan atheist 2012
## 26438 Japan non-atheist 2012
## 26439 Japan atheist 2012
## 26440 Japan atheist 2012
## 26441 Japan non-atheist 2012
## 26442 Japan non-atheist 2012
## 26443 Japan non-atheist 2012
## 26444 Japan atheist 2012
## 26445 Japan atheist 2012
## 26446 Japan non-atheist 2012
## 26447 Japan non-atheist 2012
## 26448 Japan non-atheist 2012
## 26449 Japan atheist 2012
## 26450 Japan atheist 2012
## 26451 Japan non-atheist 2012
## 26452 Japan atheist 2012
## 26453 Japan non-atheist 2012
## 26454 Japan non-atheist 2012
## 26455 Japan non-atheist 2012
## 26456 Japan non-atheist 2012
## 26457 Japan atheist 2012
## 26458 Japan non-atheist 2012
## 26459 Japan non-atheist 2012
## 26460 Japan atheist 2012
## 26461 Japan non-atheist 2012
## 26462 Japan non-atheist 2012
## 26463 Japan non-atheist 2012
## 26464 Japan atheist 2012
## 26465 Japan atheist 2012
## 26466 Japan non-atheist 2012
## 26467 Japan atheist 2012
## 26468 Japan non-atheist 2012
## 26469 Japan non-atheist 2012
## 26470 Japan atheist 2012
## 26471 Japan non-atheist 2012
## 26472 Japan non-atheist 2012
## 26473 Japan non-atheist 2012
## 26474 Japan non-atheist 2012
## 26475 Japan atheist 2012
## 26476 Japan atheist 2012
## 26477 Japan non-atheist 2012
## 26478 Japan non-atheist 2012
## 26479 Japan atheist 2012
## 26480 Japan non-atheist 2012
## 26481 Japan non-atheist 2012
## 26482 Japan non-atheist 2012
## 26483 Japan non-atheist 2012
## 26484 Japan non-atheist 2012
## 26485 Japan non-atheist 2012
## 26486 Japan non-atheist 2012
## 26487 Japan non-atheist 2012
## 26488 Japan atheist 2012
## 26489 Japan non-atheist 2012
## 26490 Japan non-atheist 2012
## 26491 Japan non-atheist 2012
## 26492 Japan non-atheist 2012
## 26493 Japan atheist 2012
## 26494 Japan non-atheist 2012
## 26495 Japan atheist 2012
## 26496 Japan atheist 2012
## 26497 Japan non-atheist 2012
## 26498 Japan non-atheist 2012
## 26499 Japan non-atheist 2012
## 26500 Japan atheist 2012
## 26501 Japan non-atheist 2012
## 26502 Japan non-atheist 2012
## 26503 Japan non-atheist 2012
## 26504 Japan atheist 2012
## 26505 Japan non-atheist 2012
## 26506 Japan atheist 2012
## 26507 Japan atheist 2012
## 26508 Japan non-atheist 2012
## 26509 Japan non-atheist 2012
## 26510 Japan non-atheist 2012
## 26511 Japan non-atheist 2012
## 26512 Japan non-atheist 2012
## 26513 Japan atheist 2012
## 26514 Japan non-atheist 2012
## 26515 Japan atheist 2012
## 26516 Japan non-atheist 2012
## 26517 Japan atheist 2012
## 26518 Japan non-atheist 2012
## 26519 Japan non-atheist 2012
## 26520 Japan atheist 2012
## 26521 Japan non-atheist 2012
## 26522 Japan non-atheist 2012
## 26523 Japan non-atheist 2012
## 26524 Japan non-atheist 2012
## 26525 Japan non-atheist 2012
## 26526 Japan non-atheist 2012
## 26527 Japan non-atheist 2012
## 26528 Japan non-atheist 2012
## 26529 Japan non-atheist 2012
## 26530 Japan non-atheist 2012
## 26531 Japan non-atheist 2012
## 26532 Japan non-atheist 2012
## 26533 Japan non-atheist 2012
## 26534 Japan atheist 2012
## 26535 Japan non-atheist 2012
## 26536 Japan non-atheist 2012
## 26537 Japan non-atheist 2012
## 26538 Japan non-atheist 2012
## 26539 Japan non-atheist 2012
## 26540 Japan non-atheist 2012
## 26541 Japan atheist 2012
## 26542 Japan non-atheist 2012
## 26543 Japan non-atheist 2012
## 26544 Japan atheist 2012
## 26545 Japan non-atheist 2012
## 26546 Japan non-atheist 2012
## 26547 Japan atheist 2012
## 26548 Japan non-atheist 2012
## 26549 Japan non-atheist 2012
## 26550 Japan atheist 2012
## 26551 Japan atheist 2012
## 26552 Japan non-atheist 2012
## 26553 Japan atheist 2012
## 26554 Japan non-atheist 2012
## 26555 Japan non-atheist 2012
## 26556 Japan non-atheist 2012
## 26557 Japan non-atheist 2012
## 26558 Japan atheist 2012
## 26559 Japan atheist 2012
## 26560 Japan non-atheist 2012
## 26561 Japan non-atheist 2012
## 26562 Japan non-atheist 2012
## 26563 Japan non-atheist 2012
## 26564 Japan atheist 2012
## 26565 Japan non-atheist 2012
## 26566 Japan non-atheist 2012
## 26567 Japan non-atheist 2012
## 26568 Japan atheist 2012
## 26569 Japan non-atheist 2012
## 26570 Japan non-atheist 2012
## 26571 Japan non-atheist 2012
## 26572 Japan atheist 2012
## 26573 Japan atheist 2012
## 26574 Japan non-atheist 2012
## 26575 Japan non-atheist 2012
## 26576 Japan non-atheist 2012
## 26577 Japan non-atheist 2012
## 26578 Japan non-atheist 2012
## 26579 Japan atheist 2012
## 26580 Japan atheist 2012
## 26581 Japan atheist 2012
## 26582 Japan atheist 2012
## 26583 Japan atheist 2012
## 26584 Japan non-atheist 2012
## 26585 Japan non-atheist 2012
## 26586 Japan non-atheist 2012
## 26587 Japan non-atheist 2012
## 26588 Japan atheist 2012
## 26589 Japan atheist 2012
## 26590 Japan non-atheist 2012
## 26591 Japan non-atheist 2012
## 26592 Japan non-atheist 2012
## 26593 Japan non-atheist 2012
## 26594 Japan non-atheist 2012
## 26595 Japan non-atheist 2012
## 26596 Japan non-atheist 2012
## 26597 Japan non-atheist 2012
## 26598 Japan non-atheist 2012
## 26599 Japan atheist 2012
## 26600 Japan non-atheist 2012
## 26601 Japan non-atheist 2012
## 26602 Japan atheist 2012
## 26603 Japan non-atheist 2012
## 26604 Japan non-atheist 2012
## 26605 Japan non-atheist 2012
## 26606 Japan atheist 2012
## 26607 Japan atheist 2012
## 26608 Japan atheist 2012
## 26609 Japan non-atheist 2012
## 26610 Japan atheist 2012
## 26611 Japan non-atheist 2012
## 26612 Japan non-atheist 2012
## 26613 Japan atheist 2012
## 26614 Japan atheist 2012
## 26615 Japan non-atheist 2012
## 26616 Japan non-atheist 2012
## 26617 Japan non-atheist 2012
## 26618 Japan atheist 2012
## 26619 Japan non-atheist 2012
## 26620 Japan atheist 2012
## 26621 Japan non-atheist 2012
## 26622 Japan atheist 2012
## 26623 Japan atheist 2012
## 26624 Japan non-atheist 2012
## 26625 Japan atheist 2012
## 26626 Japan non-atheist 2012
## 26627 Japan non-atheist 2012
## 26628 Japan non-atheist 2012
## 26629 Japan non-atheist 2012
## 26630 Japan non-atheist 2012
## 26631 Japan atheist 2012
## 26632 Japan non-atheist 2012
## 26633 Japan atheist 2012
## 26634 Japan non-atheist 2012
## 26635 Japan non-atheist 2012
## 26636 Japan atheist 2012
## 26637 Japan non-atheist 2012
## 26638 Japan non-atheist 2012
## 26639 Japan atheist 2012
## 26640 Japan non-atheist 2012
## 26641 Japan non-atheist 2012
## 26642 Japan non-atheist 2012
## 26643 Japan atheist 2012
## 26644 Japan atheist 2012
## 26645 Japan atheist 2012
## 26646 Japan non-atheist 2012
## 26647 Japan non-atheist 2012
## 26648 Japan atheist 2012
## 26649 Japan non-atheist 2012
## 26650 Japan non-atheist 2012
## 26651 Japan non-atheist 2012
## 26652 Japan non-atheist 2012
## 26653 Japan non-atheist 2012
## 26654 Japan atheist 2012
## 26655 Japan atheist 2012
## 26656 Japan non-atheist 2012
## 26657 Japan atheist 2012
## 26658 Japan non-atheist 2012
## 26659 Japan non-atheist 2012
## 26660 Japan atheist 2012
## 26661 Japan non-atheist 2012
## 26662 Japan non-atheist 2012
## 26663 Japan non-atheist 2012
## 26664 Japan atheist 2012
## 26665 Japan non-atheist 2012
## 26666 Japan non-atheist 2012
## 26667 Japan atheist 2012
## 26668 Japan atheist 2012
## 26669 Japan atheist 2012
## 26670 Japan non-atheist 2012
## 26671 Japan atheist 2012
## 26672 Japan non-atheist 2012
## 26673 Japan non-atheist 2012
## 26674 Japan non-atheist 2012
## 26675 Japan non-atheist 2012
## 26676 Japan non-atheist 2012
## 26677 Japan non-atheist 2012
## 26678 Japan non-atheist 2012
## 26679 Japan non-atheist 2012
## 26680 Japan non-atheist 2012
## 26681 Japan atheist 2012
## 26682 Japan non-atheist 2012
## 26683 Japan non-atheist 2012
## 26684 Japan non-atheist 2012
## 26685 Japan atheist 2012
## 26686 Japan atheist 2012
## 26687 Japan non-atheist 2012
## 26688 Japan atheist 2012
## 26689 Japan non-atheist 2012
## 26690 Japan non-atheist 2012
## 26691 Japan non-atheist 2012
## 26692 Japan non-atheist 2012
## 26693 Japan non-atheist 2012
## 26694 Japan atheist 2012
## 26695 Japan non-atheist 2012
## 26696 Japan non-atheist 2012
## 26697 Japan non-atheist 2012
## 26698 Japan non-atheist 2012
## 26699 Japan non-atheist 2012
## 26700 Japan non-atheist 2012
## 26701 Japan non-atheist 2012
## 26702 Japan non-atheist 2012
## 26703 Japan non-atheist 2012
## 26704 Japan non-atheist 2012
## 26705 Japan non-atheist 2012
## 26706 Japan atheist 2012
## 26707 Japan non-atheist 2012
## 26708 Japan non-atheist 2012
## 26709 Japan atheist 2012
## 26710 Japan non-atheist 2012
## 26711 Japan atheist 2012
## 26712 Japan non-atheist 2012
## 26713 Japan atheist 2012
## 26714 Japan non-atheist 2012
## 26715 Japan non-atheist 2012
## 26716 Japan atheist 2012
## 26717 Japan non-atheist 2012
## 26718 Japan atheist 2012
## 26719 Japan non-atheist 2012
## 26720 Japan non-atheist 2012
## 26721 Japan atheist 2012
## 26722 Japan atheist 2012
## 26723 Japan non-atheist 2012
## 26724 Japan non-atheist 2012
## 26725 Japan non-atheist 2012
## 26726 Japan non-atheist 2012
## 26727 Japan non-atheist 2012
## 26728 Japan atheist 2012
## 26729 Japan non-atheist 2012
## 26730 Japan non-atheist 2012
## 26731 Japan non-atheist 2012
## 26732 Japan atheist 2012
## 26733 Japan non-atheist 2012
## 26734 Japan atheist 2012
## 26735 Japan non-atheist 2012
## 26736 Japan non-atheist 2012
## 26737 Japan non-atheist 2012
## 26738 Japan non-atheist 2012
## 26739 Japan atheist 2012
## 26740 Japan non-atheist 2012
## 26741 Japan non-atheist 2012
## 26742 Japan non-atheist 2012
## 26743 Japan non-atheist 2012
## 26744 Japan atheist 2012
## 26745 Japan atheist 2012
## 26746 Japan atheist 2012
## 26747 Japan non-atheist 2012
## 26748 Japan atheist 2012
## 26749 Japan non-atheist 2012
## 26750 Japan atheist 2012
## 26751 Japan atheist 2012
## 26752 Japan non-atheist 2012
## 26753 Japan non-atheist 2012
## 26754 Japan atheist 2012
## 26755 Japan non-atheist 2012
## 26756 Japan non-atheist 2012
## 26757 Japan non-atheist 2012
## 26758 Japan non-atheist 2012
## 26759 Japan atheist 2012
## 26760 Japan non-atheist 2012
## 26761 Japan non-atheist 2012
## 26762 Japan non-atheist 2012
## 26763 Japan non-atheist 2012
## 26764 Japan atheist 2012
## 26765 Japan atheist 2012
## 26766 Japan atheist 2012
## 26767 Japan atheist 2012
## 26768 Japan non-atheist 2012
## 26769 Japan non-atheist 2012
## 26770 Japan atheist 2012
## 26771 Japan non-atheist 2012
## 26772 Japan atheist 2012
## 26773 Japan non-atheist 2012
## 26774 Japan non-atheist 2012
## 26775 Japan non-atheist 2012
## 26776 Japan non-atheist 2012
## 26777 Japan non-atheist 2012
## 26778 Japan non-atheist 2012
## 26779 Japan non-atheist 2012
## 26780 Japan atheist 2012
## 26781 Japan non-atheist 2012
## 26782 Japan non-atheist 2012
## 26783 Japan non-atheist 2012
## 26784 Japan non-atheist 2012
## 26785 Japan atheist 2012
## 26786 Japan atheist 2012
## 26787 Japan non-atheist 2012
## 26788 Japan non-atheist 2012
## 26789 Japan atheist 2012
## 26790 Japan non-atheist 2012
## 26791 Japan non-atheist 2012
## 26792 Japan atheist 2012
## 26793 Japan non-atheist 2012
## 26794 Japan non-atheist 2012
## 26795 Japan atheist 2012
## 26796 Japan non-atheist 2012
## 26797 Japan non-atheist 2012
## 26798 Japan non-atheist 2012
## 26799 Japan atheist 2012
## 26800 Japan non-atheist 2012
## 26801 Japan non-atheist 2012
## 26802 Japan atheist 2012
## 26803 Japan non-atheist 2012
## 26804 Japan atheist 2012
## 26805 Japan non-atheist 2012
## 26806 Japan non-atheist 2012
## 26807 Japan atheist 2012
## 26808 Japan atheist 2012
## 26809 Japan atheist 2012
## 26810 Japan non-atheist 2012
## 26811 Japan atheist 2012
## 26812 Japan non-atheist 2012
## 26813 Japan atheist 2012
## 26814 Japan atheist 2012
## 26815 Japan non-atheist 2012
## 26816 Japan atheist 2012
## 26817 Japan atheist 2012
## 26818 Japan non-atheist 2012
## 26819 Japan non-atheist 2012
## 26820 Japan atheist 2012
## 26821 Japan non-atheist 2012
## 26822 Japan non-atheist 2012
## 26823 Japan non-atheist 2012
## 26824 Japan non-atheist 2012
## 26825 Japan non-atheist 2012
## 26826 Japan non-atheist 2012
## 26827 Japan non-atheist 2012
## 26828 Japan non-atheist 2012
## 26829 Japan non-atheist 2012
## 26830 Japan non-atheist 2012
## 26831 Japan non-atheist 2012
## 26832 Japan non-atheist 2012
## 26833 Japan non-atheist 2012
## 26834 Japan non-atheist 2012
## 26835 Japan non-atheist 2012
## 26836 Japan non-atheist 2012
## 26837 Japan atheist 2012
## 26838 Japan atheist 2012
## 26839 Japan non-atheist 2012
## 26840 Japan non-atheist 2012
## 26841 Japan non-atheist 2012
## 26842 Japan non-atheist 2012
## 26843 Japan atheist 2012
## 26844 Japan non-atheist 2012
## 26845 Japan non-atheist 2012
## 26846 Japan non-atheist 2012
## 26847 Japan non-atheist 2012
## 26848 Japan non-atheist 2012
## 26849 Japan atheist 2012
## 26850 Japan non-atheist 2012
## 26851 Japan atheist 2012
## 26852 Japan atheist 2012
## 26853 Japan atheist 2012
## 26854 Japan non-atheist 2012
## 26855 Japan non-atheist 2012
## 26856 Japan atheist 2012
## 26857 Japan non-atheist 2012
## 26858 Japan non-atheist 2012
## 26859 Japan non-atheist 2012
## 26860 Japan non-atheist 2012
## 26861 Japan non-atheist 2012
## 26862 Japan non-atheist 2012
## 26863 Japan atheist 2012
## 26864 Japan non-atheist 2012
## 26865 Japan non-atheist 2012
## 26866 Japan non-atheist 2012
## 26867 Japan non-atheist 2012
## 26868 Japan non-atheist 2012
## 26869 Japan non-atheist 2012
## 26870 Japan atheist 2012
## 26871 Japan atheist 2012
## 26872 Japan non-atheist 2012
## 26873 Japan non-atheist 2012
## 26874 Japan atheist 2012
## 26875 Japan non-atheist 2012
## 26876 Japan non-atheist 2012
## 26877 Japan atheist 2012
## 26878 Japan non-atheist 2012
## 26879 Japan non-atheist 2012
## 26880 Japan atheist 2012
## 26881 Japan non-atheist 2012
## 26882 Japan non-atheist 2012
## 26883 Japan atheist 2012
## 26884 Japan non-atheist 2012
## 26885 Japan atheist 2012
## 26886 Japan non-atheist 2012
## 26887 Japan non-atheist 2012
## 26888 Japan atheist 2012
## 26889 Japan non-atheist 2012
## 26890 Japan non-atheist 2012
## 26891 Japan atheist 2012
## 26892 Japan non-atheist 2012
## 26893 Japan atheist 2012
## 26894 Japan atheist 2012
## 26895 Japan non-atheist 2012
## 26896 Japan atheist 2012
## 26897 Japan non-atheist 2012
## 26898 Japan atheist 2012
## 26899 Japan atheist 2012
## 26900 Japan atheist 2012
## 26901 Japan non-atheist 2012
## 26902 Japan non-atheist 2012
## 26903 Japan non-atheist 2012
## 26904 Japan non-atheist 2012
## 26905 Japan non-atheist 2012
## 26906 Japan atheist 2012
## 26907 Japan non-atheist 2012
## 26908 Japan non-atheist 2012
## 26909 Japan non-atheist 2012
## 26910 Japan non-atheist 2012
## 26911 Japan atheist 2012
## 26912 Japan non-atheist 2012
## 26913 Japan non-atheist 2012
## 26914 Japan non-atheist 2012
## 26915 Japan non-atheist 2012
## 26916 Japan non-atheist 2012
## 26917 Japan non-atheist 2012
## 26918 Japan atheist 2012
## 26919 Japan non-atheist 2012
## 26920 Japan non-atheist 2012
## 26921 Japan non-atheist 2012
## 26922 Japan non-atheist 2012
## 26923 Japan non-atheist 2012
## 26924 Japan atheist 2012
## 26925 Japan non-atheist 2012
## 26926 Japan non-atheist 2012
## 26927 Japan atheist 2012
## 26928 Japan non-atheist 2012
## 26929 Japan non-atheist 2012
## 26930 Japan atheist 2012
## 26931 Japan atheist 2012
## 26932 Japan atheist 2012
## 26933 Japan non-atheist 2012
## 26934 Japan non-atheist 2012
## 26935 Japan non-atheist 2012
## 26936 Japan non-atheist 2012
## 26937 Japan non-atheist 2012
## 26938 Japan non-atheist 2012
## 26939 Japan non-atheist 2012
## 26940 Japan non-atheist 2012
## 26941 Japan atheist 2012
## 26942 Japan non-atheist 2012
## 26943 Japan atheist 2012
## 26944 Japan non-atheist 2012
## 26945 Japan non-atheist 2012
## 26946 Japan atheist 2012
## 26947 Japan non-atheist 2012
## 26948 Japan non-atheist 2012
## 26949 Japan non-atheist 2012
## 26950 Japan atheist 2012
## 26951 Japan non-atheist 2012
## 26952 Japan non-atheist 2012
## 26953 Japan atheist 2012
## 26954 Japan atheist 2012inference(jp12$response, est = "proportion", type = "ci", method = "theoretical",
success = "atheist")## Single proportion -- success: atheist
## Summary statistics:
## p_hat = 0.3069 ; n = 1212
## Check conditions: number of successes = 372 ; number of failures = 840
## Standard error = 0.0132
## 95 % Confidence interval = ( 0.281 , 0.3329 )The conditions for inference (random sample, less than 10% of population, at least 10 successes and 10 failures) are met in both the cases mentioned above - India and Japan.
(me.india<-0.0404-0.0302)## [1] 0.0102(me.japan<-0.3329-0.3069)## [1] 0.026Margin of Error for India: 0.0102 Margin of Error for Japan: 0.026
How does the proportion affect the margin of error?
Imagine you’ve set out to survey 1000 people on two questions: are you female? and are you left-handed? Since both of these sample proportions were calculated from the same sample size, they should have the same margin of error, right? Wrong! While the margin of error does change with sample size, it is also affected by the proportion.
Think back to the formula for the standard error: \(SE = \sqrt{p(1-p)/n}\). This is then used in the formula for the margin of error for a 95% confidence interval: \(ME = 1.96\times SE = 1.96\times\sqrt{p(1-p)/n}\). Since the population proportion \(p\) is in this \(ME\) formula, it should make sense that the margin of error is in some way dependent on the population proportion. We can visualize this relationship by creating a plot of \(ME\) vs. \(p\).
The first step is to make a vector p that is a sequence from 0 to 1 with each number separated by 0.01. We can then create a vector of the margin of error (me) associated with each of these values of p using the familiar approximate formula (\(ME = 2 \times SE\)). Lastly, we plot the two vectors against each other to reveal their relationship.
n <- 1000
p <- seq(0, 1, 0.01)
me <- 2 * sqrt(p * (1 - p)/n)
plot(me ~ p, ylab = "Margin of Error", xlab = "Population Proportion")
- Describe the relationship between
pandme.
The relation between p and me is non-linear. It is quadratic because the numerator for SE has a p-squared term in it. The ME reaches its higest point when p=0.5, because that gives the largest value of the numerator in the SE term. All other values of p before and after 0.5 yield lower values of the ME.
Success-failure condition
The textbook emphasizes that you must always check conditions before making inference. For inference on proportions, the sample proportion can be assumed to be nearly normal if it is based upon a random sample of independent observations and if both \(np \geq 10\) and \(n(1 - p) \geq 10\). This rule of thumb is easy enough to follow, but it makes one wonder: what’s so special about the number 10?
The short answer is: nothing. You could argue that we would be fine with 9 or that we really should be using 11. What is the “best” value for such a rule of thumb is, at least to some degree, arbitrary. However, when \(np\) and \(n(1-p)\) reaches 10 the sampling distribution is sufficiently normal to use confidence intervals and hypothesis tests that are based on that approximation.
We can investigate the interplay between \(n\) and \(p\) and the shape of the sampling distribution by using simulations. To start off, we simulate the process of drawing 5000 samples of size 1040 from a population with a true atheist proportion of 0.1. For each of the 5000 samples we compute \(\hat{p}\) and then plot a histogram to visualize their distribution.
p <- 0.1
n <- 1040
p_hats <- rep(0, 5000)
for(i in 1:5000){
samp <- sample(c("atheist", "non_atheist"), n, replace = TRUE, prob = c(p, 1-p))
p_hats[i] <- sum(samp == "atheist")/n
}
hist(p_hats, main = "p = 0.1, n = 1040", xlim = c(0, 0.18))
These commands build up the sampling distribution of \(\hat{p}\) using the familiar for loop. You can read the sampling procedure for the first line of code inside the for loop as, “take a sample of size \(n\) with replacement from the choices of atheist and non-atheist with probabilities \(p\) and \(1 - p\), respectively.” The second line in the loop says, “calculate the proportion of atheists in this sample and record this value.” The loop allows us to repeat this process 5,000 times to build a good representation of the sampling distribution.
- Describe the sampling distribution of sample proportions at \(n = 1040\) and \(p = 0.1\). Be sure to note the center, spread, and shape.
Hint: Remember that R has functions such asmeanto calculate summary statistics.
mean(p_hats)## [1] 0.09969sd(p_hats)## [1] 0.009287382summary(p_hats)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.07019 0.09327 0.09904 0.09969 0.10577 0.12981qqnorm(p_hats)
The graph shows that the sampling distribution is normal.
- Repeat the above simulation three more times but with modified sample sizes and proportions: for \(n = 400\) and \(p = 0.1\), \(n = 1040\) and \(p = 0.02\), and \(n = 400\) and \(p = 0.02\). Plot all four histograms together by running the
par(mfrow = c(2, 2))command before creating the histograms. You may need to expand the plot window to accommodate the larger two-by-two plot. Describe the three new sampling distributions. Based on these limited plots, how does \(n\) appear to affect the distribution of \(\hat{p}\)? How does \(p\) affect the sampling distribution?
p2 <- 0.1
n2 <- 400
p2_hats <- rep(0, 5000)
for(i in 1:5000){
samp2 <- sample(c("atheist", "non_atheist"), n2, replace = TRUE, prob = c(p2, 1-p2))
p2_hats[i] <- sum(samp2 == "atheist")/n2
}
p3 <- 0.02
n3 <- 1040
p3_hats <- rep(0, 5000)
for(i in 1:5000){
samp3 <- sample(c("atheist", "non_atheist"), n3, replace = TRUE, prob = c(p3, 1-p3))
p3_hats[i] <- sum(samp3 == "atheist")/n3
}
p4 <- 0.02
n4 <- 400
p4_hats <- rep(0, 5000)
for(i in 1:5000){
samp4 <- sample(c("atheist", "non_atheist"), n4, replace = TRUE, prob = c(p4, 1-p4))
p4_hats[i] <- sum(samp4 == "atheist")/n4
}
par(mfrow = c(2, 2))
hist(p_hats, main = "p = 0.1, n = 1040", xlim = c(0, 0.18))
hist(p2_hats, main = "p2 = 0.1, n = 400", xlim = c(0, 0.18))
hist(p3_hats, main = "p3 = 0.02, n = 1040", xlim = c(0, 0.18))
hist(p4_hats, main = "p4 = 0.02, n = 400", xlim = c(0, 0.18))
#qqnorm(p_hats)
#qqnorm(p2_hats)
#qqnorm(p3_hats)
#qqnorm(p4_hats)While p impacts the center of the sampling distribution as can be expected, n controls the spread i.e. as n grows, the spread decreases.
Once you’re done, you can reset the layout of the plotting window by using the command par(mfrow = c(1, 1)) command or clicking on “Clear All” above the plotting window (if using RStudio). Note that the latter will get rid of all your previous plots.
par(mfrow = c(1, 1))- If you refer to Table 6, you’ll find that Australia has a sample proportion of 0.1 on a sample size of 1040, and that Ecuador has a sample proportion of 0.02 on 400 subjects. Let’s suppose for this exercise that these point estimates are actually the truth. Then given the shape of their respective sampling distributions, do you think it is sensible to proceed with inference and report margin of errors, as the reports does?
au12 <- subset(atheism, nationality == "Australia" & year == "2012")
ec12 <- subset(atheism, nationality == "Ecuador" & year == "2012")
inference(au12$response, est = "proportion", type = "ci", method = "theoretical",
success = "atheist")## Single proportion -- success: atheist
## Summary statistics:
## p_hat = 0.1001 ; n = 1039
## Check conditions: number of successes = 104 ; number of failures = 935
## Standard error = 0.0093
## 95 % Confidence interval = ( 0.0818 , 0.1183 )#inference(ec12$response, est = "proportion", type = "ci", method = "theoretical", success = "atheist")Based on the above, it can be seen that in the case of Ecuador, there are less than 10 successes, which violates the conditions for inference and therefore this approach is not appropriate for reporting the margin of error for Ecuador.
On your own
The question of atheism was asked by WIN-Gallup International in a similar survey that was conducted in 2005. (We assume here that sample sizes have remained the same.) Table 4 on page 13 of the report summarizes survey results from 2005 and 2012 for 39 countries.
Answer the following two questions using the
inferencefunction. As always, write out the hypotheses for any tests you conduct and outline the status of the conditions for inference.a. Is there convincing evidence that Spain has seen a change in its atheism index between 2005 and 2012?
Hint: Create a new data set for respondents from Spain. Form confidence intervals for the true proportion of athiests in both years, and determine whether they overlap.
sp05 <- subset(atheism, nationality == "Spain" & year == "2005")
sp12 <- subset(atheism, nationality == "Spain" & year == "2012")
inference(sp05$response, est = "proportion", type = "ci", method = "theoretical",
success = "atheist")## Single proportion -- success: atheist
## Summary statistics:
## p_hat = 0.1003 ; n = 1146
## Check conditions: number of successes = 115 ; number of failures = 1031
## Standard error = 0.0089
## 95 % Confidence interval = ( 0.083 , 0.1177 )inference(sp12$response, est = "proportion", type = "ci", method = "theoretical",
success = "atheist")## Single proportion -- success: atheist
## Summary statistics:
## p_hat = 0.09 ; n = 1145
## Check conditions: number of successes = 103 ; number of failures = 1042
## Standard error = 0.0085
## 95 % Confidence interval = ( 0.0734 , 0.1065 )The confidence intervals for proportion of aethists in Spain in 2005 and 2012 overlap,
**b.** Is there convincing evidence that the United States has seen a
change in its atheism index between 2005 and 2012?us05 <- subset(atheism, nationality == "United States" & year == "2005")
inference(us05$response, est = "proportion", type = "ci", method = "theoretical",
success = "atheist")## Single proportion -- success: atheist
## Summary statistics:
## p_hat = 0.01 ; n = 1002
## Check conditions: number of successes = 10 ; number of failures = 992
## Standard error = 0.0031
## 95 % Confidence interval = ( 0.0038 , 0.0161 )p.05=0.01
n05=1002
p.12=0.0499
n12=1002
(p.pooled=(10+50)/(1002+1002))## [1] 0.02994012under=((p.pooled*(1-p.pooled))/n05)+((p.pooled*(1-p.pooled))/n12)
(z.us=(p.05-p.12)/sqrt(under))## [1] -5.240415Given this z-statistic, the p-value is almost 0, and the null hypothesis (no change in proportion of atheists in the USA between 2005 and 2012) can be rejected.
- If in fact there has been no change in the atheism index in the countries listed in Table 4, in how many of those countries would you expect to detect a change (at a significance level of 0.05) simply by chance?
Hint: Look in the textbook index under Type 1 error.
39*0.05## [1] 1.95we’d expect to detect a change simply by chance in 1 country.
- Suppose you’re hired by the local government to estimate the proportion of residents that attend a religious service on a weekly basis. According to the guidelines, the estimate must have a margin of error no greater than 1% with 95% confidence. You have no idea what to expect for \(p\). How many people would you have to sample to ensure that you are within the guidelines?
Hint: Refer to your plot of the relationship between \(p\) and margin of error. Do not use the data set to answer this question.
(n=(0.5*0.5)/(0.01/1.96)^2)## [1] 9604I would have to sample at least 9,604 people.
This is a product of OpenIntro that is released under a Creative Commons Attribution-ShareAlike 3.0 Unported. This lab was written for OpenIntro by Andrew Bray and Mine Çetinkaya-Rundel.